 Several hundred students are still said to be in the complex |
Troops launched an assault as a group of students tried to leave the complex. Two students were killed, bringing the death toll to 21.
But President Pervez Musharraf has held back from a full assault, fearing casualties among women and children.
Earlier the mosque's deputy leader said he would rather die than surrender.
The BBC's Shoaib Hasan in Islamabad says a group of students tried to break out of the complex, sparking a co-ordinated assault on three sides by armoured personnel carriers and rangers.
Two students were killed in an exchange of fire and at least 10 wounded, four of them seriously.
But our correspondent says the clashes have died down and this has not been a full-scale attack.
Mosque deputy leader Abdul Rashid Ghazi said he would leave on certain conditions, including being allowed to look after his ailing mother.
Pakistani government ministers dismissed the deal and Mr Ghazi said he would not surrender unconditionally.
"We have decided that we can be martyred but we will not surrender. We are ready for our heads to be cut off but we will not bow to them," he said.
Mr Ghazi's brother Maulana Abdul Aziz - leader of the mosque - was earlier captured while trying to escape wearing a woman's burqa.
'Plane targeted'
Separately, Pakistan's media reported that Gen Musharraf's plane came under fire as it took off from a military base close to the capital.
Officials denied the reports, but police said they had found two anti-aircraft guns on a rooftop near the air base, in Rawalpindi. It was not clear if the guns had been fired.
Gen Musharraf, who has survived previous assassination attempts, was said to be unharmed.
It is believed several hundred religious students are still inside the complex, after more than 1,000 left under mounting pressure from security forces.
Officials said about 60 of those remaining are hard-liners, who have been at the vanguard of campaigning for the imposition of strict Islamic law (Sharia) in Islamabad.
The BBC's Barbara Plett in Islamabad says the government is piling psychological pressure on those still inside with a mass demonstration of force demanding unconditional surrender.
The view here is that the clerics want an honourable exit, but the president is determined to inflict absolute defeat on the Red Mosque, our correspondent says.
'Human shields'
Speaking in a telephone interview broadcast on Pakistani television, Mr Ghazi said he had told government mediator Chaudry Shujaat Hussain that his followers were ready to surrender.
But Mr Ghazi said he had insisted the authorities promise not to detain anyone who they could not prove belonged to any banned militant groups, or were not wanted for any crime.
The cleric also demanded a guarantee of safety for himself and his family, saying he wanted to remain on the premises with his sick mother until they were able to move elsewhere.
Deputy Information Minister Tariq Azim Khan said Mr Ghazi and the remaining students would have to lay down their arms unconditionally like all those who left the mosque since the violence began on Tuesday.
Earlier, Mr Khan accused the Red Mosque Islamists of using women and children as human shields, saying a number of them were being held hostage in the building's basement.