The signal of support came as Pakistan began to count the human and political cost of the bloody assault that killed the mosque's deputy leader, Abdul Rashid Ghazi, and left at least 50 armed students dead.
Eight soldiers also died in the raid, although the final death toll - including possible casualties among women and children in the mosque complex - remains unclear.
Speaking in the US state of Ohio, George Bush, the US president, signalled his support for Pakistan's government, praising the country's president, Pervez Musharraf, as "a strong ally in the war against these extremists".
Bush was speaking after the US state department signalled its backing for the raid.
"The government of Pakistan has proceeded in a responsible way. All governments have a responsibility to preserve order"
Tom Casey, US State Department
"The government of Pakistan has proceeded in a responsible way," spokesman Tom Casey said. "All governments have a responsibility to preserve order."
Meanwhile, the US embassy in Islamabad has warned its citizens in Pakistan to be on guard for the possibility of attacks by "terrorist elements" in the wake of the mosque raid.
The decision to storm the mosque followed a week-long siege and came after the government said efforts to negotiate a peaceful end had broken down.
Pakistan's interior ministry says the operation dealt a big blow to what it called Islamic hardliners and that the strong response should teach them a lesson.
But the raid has sparked protests and promises of revenge from supporters of the mosque's chief cleric.
According to military officials the body of Abdul Rashid Ghazi was found in the basement of a women's religious school after a fierce gun battle.
Troops first stormed the sprawling mosque compound before dawn on Tuesday, and 18 hours later the army said it was still trying to clear out militants from residential quarters next to the school.
Gunfire and explosions thundered over Islamabad as "Operation Silence" extended into the night.
Government spokesmen accused the fighters of holding up children and using them as human shields before and during Tuesday's raid on the mosque.
Although officials said about 30 children and 27 women had managed to escape during the fierce fighting, talks between the government and fighters suggested that hundreds had been inside.
That has raised fears that the final death toll from the military raid could rise significantly.
Some of the women in the mosque were among the most fervent supporters of the Taliban-style movement led by Lal Masjid's two cleric brothers, Abdul Aziz and Abdul Rashid Ghazi.
Aziz is reported to have escaped te mosque a week ago disguised in a woman's all-enveloping black burqa.
A high death toll from the raid could turn public opinion against Musharraf, already unpopular for attempting to fire the country's chief justice, as he seeks a second term in office in elections due later this year.
|Hundreds of students protested the |
bloody raid on the Lal Masjid [EPA]
More than 80 people have been killed since street clashes erupted on July 3 between security forces and followers of the clerics in the Red Mosque.
The cleric brothers had sought to impose strict Islamic law in the capital, including inciting students to abduct and "re-educate" alleged prostitutes.
Abdul Sattar Edhi, head of the private relief agency Edhi Foundation, said the army had asked him to prepare 400 white shrouds used for covering the dead.
Police said more than 100 armed tribesmen and religious students near Batagram, in northwest Pakistan, joined a protest over the storming of the mosque by temporarily blocking a road leading to China.
Another 500 Islamic school students in the eastern city of Multan blocked a main road and burned tyres, chanting "Down with Musharraf".