He said he was "making this offer to save the lives of the students", who were with him in the compound.
But the authorities said Abdul Rashid must come out with his followers and lay down their weapons as the violence that killed 19 people entered its fourth day.
Tariz Azeem, the deputy information minister, dismissed the offer, saying that Abdul Rashid was hiding in the mosque's basement with 20 women and an unknown number of children and could not escape justice.
Azeem said: "The time for rhetoric is over. He must come out with the women and children he is using as shields, hand over all the weapons, and bring it to a decent closure."
The tense standoff erupted on Thursday afternoon in some of the heaviest clashes yet, with students opening fire on troops and hurling hand grenades, Major-General Waheed Arshad, the chief military spokesman, said.
Two huge blasts later destroyed most of the wall surrounding the complex and sent smoke spewing into the evening sky.
Officials said security forces were using explosives to demolish the wall and had come under rocket attack.
Heavy gunfire and blasts erupted again early on Friday after nearly an eight-hour lull as armoured personnel carriers moved closer to the mosque.
"Explosive charges have been detonated by security forces to further damage and demolish the boundary wall," a security official said.
Two more blasts and heavy gunfire again erupted around 3am (2200 GMT) as sporadic firing continued.
Aftab Khan Sherpao, the country's interior minister, said there were up to 60 "hardcore" fighters in the building.
"They have AK-47s, grenades and petrol bombs. Tthey are keeping women and children who want to come out of the mosque and are not allowing them to leave," he said.
Abdul Rashid and his brother Abdul Aziz Ghazi denied that anyone was being kept against their will.
Burqa escape bid
Earlier, Abdul Aziz had called on his followers still inside the complex to surrender or flee.
|Abdul Aziz went on TV to call on followers still |
inside the mosque to surrender or flee [AFP]
Dozens of students from the mosque and its religious school had surrendered on Thursday and about 1,200 students walked out the day before in exchange for a pardon and a payment of $83 (5,000 rupees).
Tariq Azim, the deputy information minister, had said that all women and children would be granted amnesty, but men involved in killings and other crimes as well as mosque leaders would face legal action.
Abdul Aziz was arrested by security forces on Wednesday night after trying to escape the compound in a burqa, a long enveloping garment worn by Muslim women.
In an interview broadcast on state television on Thursday, he said about 850 students remained inside, including 600 women and girls, and 14 men who were armed with Kalashnikovs.
He said people still inside would not be able to hold out for long.
Smiling through much of the interview, he said he left the mosque to stop the bloodshed, and had urged others to do the same, but some women teachers had persuaded girls to stay behind.
The siege began when the Pakistani army surrounded the mosque on Wednesday, a day after at least 16 people were killed in clashes between security forces and armed activists from the mosque.
Liberal politicians had been pressing Pervez Musharraf, Pakistan's president, for months to crack down on the brothers running the Red mosque.
Musharraf himself has accused the mosque of sheltering al-Qaeda members.
The students carried out a series of provocative acts over the past six months, demanding the enforcement of Islamic law, and running a vigilante anti-vice campaign.
Source: Al Jazeera and agencies