Boko Haram fighters were patrolling the streets of Bama, preventing people from burying the dead, Ahmed Zanna said.
On Wednesday, the state government denied the town had fallen.
Officials said about 26,000 people had been displaced by fighting in Bama, a key town in the battle for control of Nigeria's north-eastern Borno state.
Earlier this week, the Nigeria Security Network (NSN) think-tank said the group had made "lightning territorial gains" 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.
Who are Boko Haram?
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.
On Wednesday, Borno state deputy governor Zannah Umar Mustapha denied the militants had taken over Bama, which had a population of about 270,000.
He told the BBC Hausa service that the army was still fighting them.
The government's National Emergency Management Agency (Nema) said on Wednesday that 26,391 had been displaced by the fighting.
"The number is growing by the hour," its spokesman Abdulkadir Ibrahim told Reuters news agency.
Bodies remain littered on the streets of a northern Nigerian town two days after it was seized by militant Islamists, a lawmaker has told the BBC.