Supporters of ousted Egyptian President Mohammed Morsi have been preparaing for action from the interim authorities after reports emerged of plans to break up two protest camps.
An interior ministry source said an operation would begin just before dawn.
But there was no sign of police activity at the sit-ins outside the Rabaa al-Adawiya mosque in eastern Cairo and at Nahda Square, to the west.
The Muslim Brotherhood, to which Mr Morsi belongs, has warned of bloodshed.
More than 250 people, most of them Morsi supporters, have already been killed in clashes since the military deposed Egypt’s first democratically elected leader on 3 July after mass protests demanding his resignation.
On Sunday night, a source from the interior ministry told the BBC an operation to disperse the two protest camps would begin shortly before dawn on Monday, and was likely to be a “gradual” process.
But as the sun rose above the capital, there were no signs of any movement from security forces personnel.
BBC correspondent James Reynolds, who was close to the Rabaa al-Adawiya mosque as dawn broke, said no activity had been seen from the security forces.
The camp around the mosque at Rabaa al-Adawiya is surrounded by military sites, and sits on what would normally be a busy dual carriageway.
Security forces had been thought likely to begin by surrounding both areas, in order to restrict access and stop anyone entering. Shipments of food and water could also be cut off.
Protesters have piled sandbags and big rocks around the sit-in, while men wearing motorcycle helmets and carrying sticks have been deployed in anticipation of a raid.
Although it was too soon to tell whether the reported break-up of the camps would not happen, there were elements in the interim government that did not want a violent end to the stand-off, our correspondent said.
Street vendors have said they have sold hundreds of gas masks.
“We are staying and are psychologically prepared for anything, and have secured the protests areas and their entrances and exits,” one of the protesters, Mustafa al-Khateeb, told the Reuters news agency.
Our correspondent says that elements in the interim Egyptian government do not want a violent end to the stand-off.
It was not clear whether the warning from the authorities was a way of again encouraging at least some protesters to leave, though earlier government attempts at persuasion have failed.
For its part, the Muslim Brotherhood has put out its own state of alert, and appears to be asking its followers to stage fresh sit-ins at other main squares in Cairo, she adds.
“We want to send a message to the coup leaders: the Egyptian people insist on continuing their revolution… And the people will insist on turning out in all squares,” senior Muslim Brotherhood official Farid Ismail said.
On Sunday, defiant Morsi supporters called for fresh street protests.
“Sisi is a traitor, Sisi is a killer,” shouted women who took part in a march through central Cairo, referring to the head of the armed forces, Gen Abdul Fattah al-Sisi.
Our correspondent says the stage is now set for confrontation, and while it is possible that the riot police may try a more nuanced approach, many fear that more blood could be shed.
Over the weekend, the grand imam of al-Azhar, Egypt’s top Islamic institution, invited prominent figures to join a meeting on national reconciliation on Monday and discuss his “compromise formula”.
The Brotherhood’s Freedom and Justice Party (FJP), told the BBC that it was ready for “any kind of dialogue with any intermediary”, but questioned Sheikh Ahmed al-Tayyib’s impartiality.
The grand imam supported the military intervention to remove Mr Morsi.
Last week, Egypt’s interim President, Adly Mansour, blamed the Muslim Brotherhood for the failure of mediation efforts by international diplomats.