At least 30 people were killed when Boko Haram Islamic extremists struck the north-east Nigerian city of Maiduguri with rocket-propelled grenades and multiple suicide bombers, witnesses said.

The military said there were multiple attacks at four south-western entry points to the city, including a woman suicide bomber who killed one other person and injured 13 gathered outside a mosque after dawn prayers on Monday.

The attack appears to be a challenge to President Muhammadu Buhari's declaration last week that Boko Haram has been "technically" defeated, capable of no more than suicide bombings on soft targets.

Nigerian troops "intercepted and destroyed" 10 suicide bombers and repelled the attackers, according to PR Nigeria, an agency that disseminates government news.

Maiduguri is the birthplace of Boko Haram, which emerged as a much more radical entity after Nigerian security forces launched an all-out assault on their compound in the city, killing 700 people in 2009.

Militants firing indiscriminately from the back of three trucks attacked the outlying village of Dawari, soldiers engaged them and, as people were fleeing, a woman ran into the area yelling "Boko Haram, Boko Haram". When people gathered, she detonated herself, according to village head Bulama Isa.

A rocket-propelled grenade exploded, setting grass-thatched huts on fire, and a second woman blew herself up, according to Isa.

Meanwhile, in Duwari, an outlying suburb of Maiduguri, the village chief, 10 of his children and others were killed, according to residents Ahmed Bala and Umar Ibrahim.

A soldier said the insurgents fired rocket-propelled grenades into four residential areas on the outskirts of the city. Soldiers fired back, and many civilians were caught in the crossfire, according to the soldier.

A nurse and a guard at Maiduguri Specialist Hospital said at least 20 other bodies arrived overnight and dozens of critically injured, mainly children and women, may not survive.

Major General Lamidi Adeosun, the commander prosecuting Nigeria's war against Boko Haram, told reporters that 29 people had been killed and 88 injured in attacks which began on Sunday night.

The nurse said the hospital was so overflowing with patients that some had to be cared for in the maternity ward. About 60 people had wounds from bullets and shrapnel from explosive devices, she said. Other casualties had to be sent to other hospitals in the city.

Among those at the Specialist Hospital was a baby found dead, still tied to the back of her mother, after being hit by shrapnel, the nurse said.

It was difficult to do a body count because so many had been blown into pieces, she said, describing torsos and dismembered arms and legs.

The guard said he counted about 70 people who arrived overnight, most of them lifeless.

"The troops laid ambush on the terrorists' suspected routes ... The suicide bombers were intercepted in three different locations approaching the city," PR Nigeria said, quoting the military.

Some slipped through. Three suicide bombers blew themselves up at a home near Bakassi Estate, killing 18 people on Sunday evening, a soldier told the Associated Press.

Maiduguri, a city of about one million people, now hosts almost as many refugees, among 2.5 million people driven from their homes in the six-year-old uprising.

About 20,000 people have been killed in Nigeria and hundreds others elsewhere as the insurgents have carried their conflict across its borders into Cameroon, Niger and Chad.