1 February 2015
Last updated at 04:46 ET
It comes a week after Boko Haram's last attempt to capture the capital of Borno state was repelled by the Nigerian army with heavy loss of life.
Boko Haram began guerrilla operations in 2009 to create an Islamic state.
It has taken control of many towns and villages in north-eastern Nigeria in the last year.
The conflict has displaced at least 1.5 million people, while more than 2,000 were killed last year.
'In fear' Residents in Maiduguri told the AFP news agency that the attack began at 03:00 (02:00 GMT) and that heavy fighting is taking place on the southern edge of the city between insurgents and troops supported by vigilantes who recently have taken a central role in fighting the militants.
The security forces have not so far commented on the latest fighting, Their handling of the six-year insurgency has often been criticised and the loss of Maiduguri would be another major setback.
"The whole city is in fear," resident Adam Krenuwa was quoted as saying. "People are afraid of what will happen if Boko Haram defeats the security forces."
The Nigerian Premium Times newspaper reported that heavy artillery could be heard in Maiduguri as the militants attacked the city from four directions.
Boko Haram at a glance
Who are Boko Haram?
Why Nigeria has not defeated Boko Haram
Boko Haram's last attempt to take over Maiduguri a week ago was stopped by the military.
But the militants did succeed in capturing the town of Monguno - 125km (80 miles) outside the city and took over a military base.
With the insurgents gaining more and more territory Maiduguri - home to tens of thousands of people who have fled their homes because of the conflict - has been increasingly vulnerable.
Aid agencies have warned that the fall of the city would trigger a humanitarian disaster.
Analysts say that the rebels are stepping up their attacks ahead of elections in Nigeria on 14 February.
President Goodluck Jonathan declared a state of emergency in Borno and two neighbouring states in 2013, vowing to defeat the militants.
However, Boko Haram has stepped up attacks since then and there are fears that many people in the north-east will not be able to vote in the election because of the conflict.
The African Union (AU) has this week backed plans for a West African task force of 7,500 troops to fight Boko Haram.
Four of Nigeria's neighbours - Benin, Cameroon, Chad and Niger - have agreed to contribute troops.
Are you in the area? Email haveyoursay@bbc.co with your experiences.
Have your say
by Rashida Adjani and Biodun Iginla, BBC News, N'Djamena, Chad
Boko
Haram Islamist militants have launched a fresh assault on the
strategically important Nigerian city of Maiduguri, eyewitnesses say.
Gunfire was reported on the streets of the northern city after an attack that began in the early hours of Sunday.It comes a week after Boko Haram's last attempt to capture the capital of Borno state was repelled by the Nigerian army with heavy loss of life.
Boko Haram began guerrilla operations in 2009 to create an Islamic state.
It has taken control of many towns and villages in north-eastern Nigeria in the last year.
The conflict has displaced at least 1.5 million people, while more than 2,000 were killed last year.
'In fear' Residents in Maiduguri told the AFP news agency that the attack began at 03:00 (02:00 GMT) and that heavy fighting is taking place on the southern edge of the city between insurgents and troops supported by vigilantes who recently have taken a central role in fighting the militants.
The security forces have not so far commented on the latest fighting, Their handling of the six-year insurgency has often been criticised and the loss of Maiduguri would be another major setback.
"The whole city is in fear," resident Adam Krenuwa was quoted as saying. "People are afraid of what will happen if Boko Haram defeats the security forces."
The Nigerian Premium Times newspaper reported that heavy artillery could be heard in Maiduguri as the militants attacked the city from four directions.
Boko Haram at a glance
- Founded in 2002, initially focused on opposing Western-style education - Boko Haram means "Western education is forbidden" in the Hausa language
- Launched military operations in 2009 to create Islamic state
- Thousands killed, mostly in north-eastern Nigeria - has also attacked police and UN headquarters in capital, Abuja
- Has abducted hundreds, including at least 200 schoolgirls
- Controls several north-eastern towns
- Has launched attacks on Cameroon
Who are Boko Haram?
Why Nigeria has not defeated Boko Haram
Boko Haram's last attempt to take over Maiduguri a week ago was stopped by the military.
But the militants did succeed in capturing the town of Monguno - 125km (80 miles) outside the city and took over a military base.
With the insurgents gaining more and more territory Maiduguri - home to tens of thousands of people who have fled their homes because of the conflict - has been increasingly vulnerable.
Aid agencies have warned that the fall of the city would trigger a humanitarian disaster.
Analysts say that the rebels are stepping up their attacks ahead of elections in Nigeria on 14 February.
President Goodluck Jonathan declared a state of emergency in Borno and two neighbouring states in 2013, vowing to defeat the militants.
However, Boko Haram has stepped up attacks since then and there are fears that many people in the north-east will not be able to vote in the election because of the conflict.
The African Union (AU) has this week backed plans for a West African task force of 7,500 troops to fight Boko Haram.
Four of Nigeria's neighbours - Benin, Cameroon, Chad and Niger - have agreed to contribute troops.
Are you in the area? Email haveyoursay@bbc.co with your experiences.
Or use the link below to leave a comment.
Boko Haram
From other news sites
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Russia Today Boko Haram opens fresh attack on major Nigeria city of Maiduguri 1 hr ago
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Mail Online UK Boko Haram launches new assault on key Nigeria city Maiduguri 1 hr ago
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Guardian.co.uk Nigeria Fight against Boko Haram to be bolstered by 7,500 African Union troops 10 hrs ago
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The Scotsman Chad attack clears fanatics from Nigerian town 33 hrs ago
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International Business Times UK Boko Haram releases pictures of child soldier training camp in Nigeria 28 Jan 2015
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