Boko Haram says it is fighting against Western education. It believes Nigeria's government is being corrupted by Western ideas and wants to see Taliban-style rule imposed across Nigeria.
More than 200 people have been killed in four days of clashes since an estimated 1,000 well-armed militants began attacking police stations and government buildings in Maiduguri.
President Umaru Yar'Adua earlier ordered Nigeria's national security agencies to take all necessary action to contain and repel attacks by the extremists.
The officer commanding the operation, Col Ben Ahanotu, said on Wednesday night: "We have taken over their enclave, they are on the run and we are going after them," reports AFP news agency.
The military told the BBC personal items found on the bodies of young men indicated that many had come from neighbouring Chad and Niger.
Security forces flooded into Maiduguri and began shelling sect leader Mohammed Yusuf's compound on Tuesday.
Fierce fighting continued through the night and into Wednesday with the militants returning heavy gunfire.
Pictures from Monday in Bauchi show the aftermath of violence
Also on Wednesday, police freed about 100 women and children who were being held by the sect in a building in Maiduguri.
The captives told the BBC they had been held for six days, living on dates and water.
Many of the women said their husbands were Boko Haram followers, and they had been forced to travel to Maiduguri from other parts of Nigeria.
Four states in northern Nigeria have been affected by Boko Haram unrest - Borno, Bauchi, Kano and Yobe.
A total of 103 deaths were officially reported in Maiduguri and reports say more than 50 people died in Bauchi and Yobe, but the true number of casualties may be much greater. There were also reports of Christian churches being torched.
Sharia law is in place across northern Nigeria, but there is no history of al-Qaeda-linked violence in the country.
The country's 150 million people are split almost equally between Muslims in the north and Christians in the south.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.