Two air force jets and a helicopter repeatedly flew low over Tahrir (Liberation) Square, the main gathering point for demonstrators.
A column of tanks arrived there only to have its path blocked by protesters.
Amid the stand-off, leading opposition figure Mohamed ElBaradei arrived in Tahrir Square to address protesters.
"You have taken back your rights and what we have begun cannot go back," he said, quoted by Reuters news agency.
"I bow to the people of Egypt in respect. I ask of you patience, change is coming in the next few days."
Meanwhile, US Secretary of State Hillary Clinton has called for an "orderly transition" of power in Egypt.
She told ABC News that Washington wanted to see change that would bring about a democratic government.
"We want to see restraint, we do not want to see violence by any security forces," she added.
Defiance
The demonstrators are defying a curfew that began at 1600 (1400 GMT).
The BBC's Jeremy Bowen, in Tahrir Square, says there is a mood of defiance among protesters, who are accusing the military of trying to intimidate them.
The arrival of the tanks and the buzzing of the square by the jets significantly raised the tension among the thousands gathered.
Continue reading the main story
AT THE SCENE
Yolande Knell BBC News, Cairo
People in central Cairo stopped and stared as fighter jets flew overhead. This was a sight few had seen before. It was a clear display of military might, a strong reminder that the military remains the most powerful institution in Egypt.
Speculation and unsubstantiated rumours constantly circulate. Some are certain the president is stepping down. Others have heard of government figures being arrested. It all adds to the sense of insecurity.
Most shops and businesses are closed and now many ordinary Egyptians are starting to panic. There are already reports of bread shortages as long queues exhaust supplies. In one large supermarket I saw people clearing the shelves. One woman told me she was preparing to spend several days locked in her apartment if events took a turn for the worse.
At a cash machine outside a bank, two housewives emptied their accounts, filling their bags with money.
Earlier, despite the presence of armoured vehicles, protesters appeared to have free rein in the city centre, with no sign of the riot police with whom they have clashed violently in recent days.
At one point, an army officer was carried aloft on the shoulders of cheering protesters.
The police have largely disappeared from the streets.
Clashes are reported to have left at least 100 people dead since rallies began on Tuesday in cities including Cairo, Suez and Alexandria. Thousands have been injured.
Meanwhile, al-Jazeera's broadcasts via an Egyptian satellite have been halted. The Egyptian government earlier ordered the Arabic TV channel, which has been showing blanket coverage of the protests, to shut down its operations in the country.
Sunday is the start of the working week in the Middle East, but many businesses in the capital are closed. Internet access remains intermittent.
Throughout the city, armed citizens' groups have formed to respond to widespread looting and disorder.
In the northern coastal city of Alexandria, thousands of anti-government protesters marched on a mosque for the funerals of two demonstrators killed in clashes with police the previous day.
The BBC's John Simpson, in Alexandria, reports a heavy military presence and a tense atmosphere in the city.
Across Egypt, thousands of prisoners are reported to have escaped from jails after overpowering their guards.
Travel advice
President Mubarak earlier met top commanders during a visit to a military headquarters. He has appointed a vice-president - intelligence chief Omar Suleiman - as he struggles to regain control. Aviation Minister Ahmed Shafiq has been appointed prime minister.
Continue reading the main story
Protesters stop tanks in Tahrir Square
* In pictures: Egypt protests, day six
Sunday saw a number of Egyptian political movements issue a joint statement calling on Mr ElBaradei - a Nobel peace laureate - to form a transitional government.
Israeli Prime Minister Benjamin Netanyahu has said his government is watching events in Egypt carefully, and hoping to maintain peaceful relations with its Arab neighbour.
The Rafah crossing between Egypt and the southern Gaza Strip is closed, Palestinian officials say.
The US government, which previously advised US citizens against non-essential travel to Egypt, is now advising Americans in Egypt to consider leaving the country as soon as possible.
The UK also advised its nationals in Cairo, Alexandria and Suez to leave if it is safe for them to do so.
A number of other European countries have also advised against visiting the country.
The unrest in Egypt follows an uprising in Tunisia two weeks ago which toppled President Zine al-Abidine Ben Ali after 23 years in power.
The Tunisian upheaval began with anger over rising food prices, high unemployment and anger at official corruption - problems which have also left many people in Egypt feeling frustrated and resentful of their leadership.
A column of tanks arrived there only to have its path blocked by protesters.
Amid the stand-off, leading opposition figure Mohamed ElBaradei arrived in Tahrir Square to address protesters.
"You have taken back your rights and what we have begun cannot go back," he said, quoted by Reuters news agency.
"I bow to the people of Egypt in respect. I ask of you patience, change is coming in the next few days."
Meanwhile, US Secretary of State Hillary Clinton has called for an "orderly transition" of power in Egypt.
She told ABC News that Washington wanted to see change that would bring about a democratic government.
"We want to see restraint, we do not want to see violence by any security forces," she added.
Defiance
The demonstrators are defying a curfew that began at 1600 (1400 GMT).
The BBC's Jeremy Bowen, in Tahrir Square, says there is a mood of defiance among protesters, who are accusing the military of trying to intimidate them.
The arrival of the tanks and the buzzing of the square by the jets significantly raised the tension among the thousands gathered.
Continue reading the main story
AT THE SCENE
Yolande Knell BBC News, Cairo
People in central Cairo stopped and stared as fighter jets flew overhead. This was a sight few had seen before. It was a clear display of military might, a strong reminder that the military remains the most powerful institution in Egypt.
Speculation and unsubstantiated rumours constantly circulate. Some are certain the president is stepping down. Others have heard of government figures being arrested. It all adds to the sense of insecurity.
Most shops and businesses are closed and now many ordinary Egyptians are starting to panic. There are already reports of bread shortages as long queues exhaust supplies. In one large supermarket I saw people clearing the shelves. One woman told me she was preparing to spend several days locked in her apartment if events took a turn for the worse.
At a cash machine outside a bank, two housewives emptied their accounts, filling their bags with money.
Earlier, despite the presence of armoured vehicles, protesters appeared to have free rein in the city centre, with no sign of the riot police with whom they have clashed violently in recent days.
At one point, an army officer was carried aloft on the shoulders of cheering protesters.
The police have largely disappeared from the streets.
Clashes are reported to have left at least 100 people dead since rallies began on Tuesday in cities including Cairo, Suez and Alexandria. Thousands have been injured.
Meanwhile, al-Jazeera's broadcasts via an Egyptian satellite have been halted. The Egyptian government earlier ordered the Arabic TV channel, which has been showing blanket coverage of the protests, to shut down its operations in the country.
Sunday is the start of the working week in the Middle East, but many businesses in the capital are closed. Internet access remains intermittent.
Throughout the city, armed citizens' groups have formed to respond to widespread looting and disorder.
In the northern coastal city of Alexandria, thousands of anti-government protesters marched on a mosque for the funerals of two demonstrators killed in clashes with police the previous day.
The BBC's John Simpson, in Alexandria, reports a heavy military presence and a tense atmosphere in the city.
Across Egypt, thousands of prisoners are reported to have escaped from jails after overpowering their guards.
Travel advice
President Mubarak earlier met top commanders during a visit to a military headquarters. He has appointed a vice-president - intelligence chief Omar Suleiman - as he struggles to regain control. Aviation Minister Ahmed Shafiq has been appointed prime minister.
Continue reading the main story
Protesters stop tanks in Tahrir Square
* In pictures: Egypt protests, day six
Sunday saw a number of Egyptian political movements issue a joint statement calling on Mr ElBaradei - a Nobel peace laureate - to form a transitional government.
Israeli Prime Minister Benjamin Netanyahu has said his government is watching events in Egypt carefully, and hoping to maintain peaceful relations with its Arab neighbour.
The Rafah crossing between Egypt and the southern Gaza Strip is closed, Palestinian officials say.
The US government, which previously advised US citizens against non-essential travel to Egypt, is now advising Americans in Egypt to consider leaving the country as soon as possible.
The UK also advised its nationals in Cairo, Alexandria and Suez to leave if it is safe for them to do so.
A number of other European countries have also advised against visiting the country.
The unrest in Egypt follows an uprising in Tunisia two weeks ago which toppled President Zine al-Abidine Ben Ali after 23 years in power.
The Tunisian upheaval began with anger over rising food prices, high unemployment and anger at official corruption - problems which have also left many people in Egypt feeling frustrated and resentful of their leadership.
