Pakistan's President Pervez Musharraf has told security forces to be patient to allow women to leave the Red Mosque complex (Lal Masjid) in Islamabad.
He ordered a temporary halt to the security operation in the stand-off between radicals and the authorities.
However the deputy leader of the mosque said he and his militant followers would rather die than surrender.
Ghazi Abdul Rashid made the defiant statement as the stand-off, in which 19 have died, entered its fourth day.
"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.
There was no immediate official response. An earlier offer of conditional surrender made by Mr Ghazi on Thursday was rejected by Pakistani government ministers.
The offer to end the confrontation came after Mr Ghazi's brother was captured while trying to flee the mosque.
Pakistani troops have pounded the Red Mosque complex, breaching its wall in three places. On Thursday evening much of the city was plunged into darkness, after storms caused failures in the power supply.
Speaking in a telephone interview broadcast on Pakistani television, Abdul Rashid said he had told government mediator Chaudry Shujaat Hussain that his followers were ready to surrender.
"I am making this offer to save the lives of the students," he said.
But Abdul Rashid 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.
"If they are linked to any banned organisation, it can be verified," he said
"It can be looked into... those who are not should be let go."
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.
The Pakistani government rejected Abdul Rashid's conditional offer and Deputy Information Minister Tariq Azim Khan said he and the remaining students would have to lay down their arms unconditionally like all those who left the mosque over the past two days.
"He should allow everybody, women, children to come out. He can come out with them... nobody is going to fire on them," he told Reuters.
"He should surrender himself... If there are cases against him, let the court decide."
The minister said Abdul Rashid was involved in a number of criminal cases.
Earlier, Mr Khan accused the Red Mosque Islamists of using women and children as human shields.
"A large number of women and children are being held hostage by armed men in room," he told a press conference.
The Interior Minister, Aftab Sherpao, said 740 men and 400 women had so far left the mosque.
Mr Sherpao said he believed 300-400 students were still inside, of whom around 50-60 were hardcore militants.
The clerics and their followers have been campaigning for Islamic Sharia law in Islamabad.
The BBC's Barbara Plett in Islamabad says the radicals do not have much support in the capital and people are quite glad to see the government taking them on.
But the authorities' action is likely to upset people in the more conservative North-West Frontier province, where most of the students come from.