Boko Haram fighters were patrolling the streets of Bama, preventing people from burying the dead, Ahmed Zanna said.
The militants captured the town on Tuesday after a fierce battle with government forces.
Bama is the biggest town under Boko Haram’s control. It is fighting for an Islamic state in Nigeria.
On Wednesday, the Nigeria Security Network (NSN) think-tank said the group had made “lightning territorial gains” in north-eastern Nigeria’s Borno state in recent months, raising fears that the country could disintegrate like Syria and Iraq, where the Islamic State (IS) rebel group has declared a caliphate.
Boko Haram has also said it has set up a caliphate in the areas it controls – it is not clear if the two groups are allied.
Mr Zanna, a senator in Borno, said the humanitarian situation in Bama was “terrible” and there had been a “lot of killings” in the town.
“So many bodies litter the streets, and people are not allowed to even go and bury the dead ones. So the situation is getting worse and worse,” Mr Zanna told the BBC’s Newsday programme after speaking to a resident who fled the town.
Boko Haram has captured a string of towns in northern-eastern Nigeria in recent months, fuelling concern that it could advance towards the main city, Maiduguri.
Mr Zanna said it would be “catastrophic” if Boko Haram launched an assault on Maiduguri, which has a population of more than two million.
“I’m begging the government to send more troops and armoury to Maiduguri,” he said.
“Boko Haram do come overwhelmingly because they recruited en masse in the villages [in Borno state],” he added. .
Mr Zanna said government forces had “gallantly” defended Bama, before it fell to Boko Haram.
Residents told BBC Hausa that Boko Haram returned to the town on Tuesday with reinforcements after being repelled by government forces the previous day.
The government has not commented on the fall of Bama.
It had a population of population of about 270,000, but thousands of people have fled the town.
About 10,000 people have fled northern Nigeria for neighbouring states in the past week as fighting escalates, aid workers say.