The blasts in Maiduguri and dawn raid in Damaturu came just days after a deadly mosque attack in the northern city of Kano left at least 120 people dead and hundreds more injured.
Almost daily attacks have heightened tensions in Nigeria's far northeast and sparked fears of unrest beyond the country's borders.
Both Maiduguri, which is the capital of Borno state, and Damaturu, the main city in neighbouring Yobe, have been hit repeatedly by Boko Haram.
The site of the latest blasts in Maiduguri -- the popular Monday Market -- was hit just last Tuesday when two women detonated explosives among the crowds of shoppers.
In that attack, more than 45 people were killed.
Two suspected female suicide bombers were then arrested in the city on Wednesday and Thursday, while on Friday, a roadside bomb near another market was defused.
Boko Haram claimed responsibility for a similar raid in Damaturu on October 24, 2013, in which four police buildings were hit with guns and explosives and militants battled with security forces.
Both incidents will add to claims that Nigeria's government has not done enough to protect civilians from the militants, whose insurgency has claimed over 13,000 lives since it began in 2009.
- Market blasts -
In Maiduguri, Borno state police spokesman Gideon Jibrin initially said that more than 10 people were killed and many more were injured, but he later changed the toll.
"The casualty figure is five dead and not as earlier sent," he said in a text message.
A previous text said that two female suicide bombers detonated their explosives in two different areas of the market, after initial reports of a single middle-aged woman and two blasts.
One rescue official also said that five people had died and 47 were injured.
But one witness at the scene, Goni Abba, said he counted "10 dead bodies".
- 'Serious situation' -
In Damaturu, residents in the Gujba Road area of the city were jolted out of bed by the sound of gunshots and explosions at about 4:45 am (0345 GMT) and many fled.
"The gunmen came in numbers. They have burnt down the police barracks.... We have left our home. We are now in the bush. We don't know what's going to happen," said one local, Umar Sada.
Another local resident, a government official who asked not to be identified, said: "It's chaos all over the town.
"All I can hear is explosions and gunfire from my house. I couldn't go out for morning prayers because this started before dawn and I'm afraid to leave in case I get caught up in it."
There was no immediate comment from the military in Damaturu, where government troops are also stationed, or from Abuja, although air force jets were seen overhead.
But the Yobe state police commissioner, Marcus Danladi, said they were dealing with a "serious situation". Civilian vigilantes in the city claimed that more than 40 Boko Haram fighters were killed.
A staff member at the federal polytechnic in Damaturu said the fighting was still raging by mid-morning and some shells had landed in the university compound.
Other residents said fighting was taking place near detention facilities where Boko Haram suspects are being held near the state governor's residence, and the jets were bombarding the militants.