Armed men on Sunday hit Maiduguri's south in a bid to gain entry to the strategically-important city. The attack on the state capital comes just two weeks before national elections are due to be held in Nigeria.
Al Jazeera's Ahmed Idriss, reporting from Abuja, said people were fleeing the south, but also moving into Maiduguri from the surrounding areas, fearing fresh attacks from other directions.
"The fighting started at about 2:00 GMT," he said.
"The military also says it is deploying large numbers of troops to the north of the city as this could be a ploy or diversion by Boko Haram," he added.
Idriss added the attack could be an attempt by the group to "prove a point" following recent successes by multinational forces fighting Boko Haram in Chad and Cameroon.
After heavy fighting in the Mulai area just three kilometres south of the city, troops backed by vigilantes repelled the attack, but the fighters then began a separate assault to the east and gun battles were ongoing, multiple witnesses said.
"The gunmen were initially subdued in Mulai, but now they have changed strategy and are attacking through the Damboa road (to the east)," local Bukar Mungono said in an account supported by two others.
"Fighting is still going on," he told AFP news agency.
Boko Haram's last attempt to take over Maiduguri just seven days ago was repelled by the military.
Following the failure of the January 25 assault, the group captured the town of Monguno, 125km from the city, and seized a military base in the area.
The most recent assault comes a day after the Chadian military said it had killed 123 rebels in two days of fighting in northern Cameroon and had launched air strikes against the Nigerian town of Gamboru.