"We have received a dead body this morning. The victim is a 22-year-old who received gunshots," a hospital doctor said.
"The deadline has expired but we are not going to start any action immediately. We do not want bloodshed. We are reasonably sure that better sense will prevail," said Khalid Pervez, the capital's top security official.
However, more than 340 of their followers surrendered, Pervez said.
As the deadline passed, Abdul Rashid Ghazi, the mosque's deputy leader, said he was prepared to talk with the government but added, "We will continue to defend ourselves".
"The deadline has expired but we are not going to start any action immediately. We do not want bloodshed. We are reasonably sure that better sense will prevail,"
Islamabad's top security official
Ghazi told a local television channel that he was not aware of any surrender deadline.
Those who surrendered came from the mosque and an adjacent seminary for women, Pervez said.
Soldiers continued to enforce a shoot-on-sight curfew around the mosque and killed a male student and an apparently mentally ill man in the early hours of the day.
Male students fought gunbattles with security forces on Tuesday in a bloody climax to the mosque's six months of defiance against the authorities.
Up to two dozen people have been killed in the clashes, with four students dying on Wednesday.
Deaths in hospital
Three others died in hospital overnight from injuries sustained a day before, medics said.
Three other wounded students were treated at the state-run Pakistan Institute of Medical Sciences early on Wednesday, a doctor at the hospital's emergency ward said.
Three others with serious bullet injuries were brought to another state-run hospital, the Polyclinic, a doctor there said.
"One of them is undergoing surgery at the operation theatre," he said.
As well as the deaths, more than 120 were wounded in the fighting on Tuesday, officials and hospitals said.
In recent months, the Lal Masjid mosque has been put under increasing pressure by Pakistani authorities.
The mosque started an anti-vice campaign is Islamabad six months ago, with its students abducting women they saw as immoral acts.
Pakistani authorities closed the mosque's radio station in March, and the government rejected a subsqeuent attempt by the mosque to form new Islamic courts.
In May, several policemen were abducted by the mosque's students and held captive. They were later released.
Pervez Musharraf, Pakistan's president, has also accused the mosque of sheltering al-Qaeda members.
About 5,000 students, most from poor areas of Pakistan, are registered at the mosque and its affiliated schools.
Elsewhere in Pakistan, a suicide bomber targeted a military convoy, killing himself and eight others.
Six soldiers and two children are understood to have died when the bomber drove his explosives filled car into the convoy in the northwestern town of Bannu on Wednesday.
"Four soldiers and a child were killed on the spot in the attack," an intelliegence official told Reuters, adding that two soldiers and a child died later in hospital.
It is unknown if the attack has any link to the siege at the Lal Masjid in Islamabad.
Clerics associated with the mosque had threatened suicide bombings in the past should force be used against them, and many of the mosque's members come from towns like Bannu.