DHAKA (Reuters) - Bangladesh police has detained the chairman and managing director of a garment factory after a fire killed seven workers, police said on Wednesday, following allegations that the plant employed under-age workers and had no license to run.

The fire at the Smart Exports Garment Ltd in the capital Dhaka on Saturday came just two months after the country's worst factory blaze turned the spotlight on the conditions in the garment sector. At least 112 people died in that fire in another part of the city.

The arrests were made on Tuesday night after the father of one of the victims filed a complaint alleging negligence, said police deputy commissioner Mollah Nazrul Islam.

"Survivors said the factory's only exit was locked when the fire started during lunch break and there was no emergency exit or any fire equipments in the two-storey building," Islam said.

He said the plant was operating without clearance from the fire department.

Officials at the factory were not immediately available for comment.

Bangladesh law requires factories to have more than one exit routes, fire alarm and fire-fighting tools, which many factories do not comply with, police and firefighters say.

Police said among the seven dead in the Smart factory, two were aged 15 and 16.

"Employing under-age boys and girls is a violation of law, said Azizul Haque, another police officer. The minimum age for employment is 18.

Working conditions at Bangladeshi factories are notoriously poor, with little enforcement of safety laws. Overcrowding and locked fire doors are common.

An official report into the blaze in November concluded it was the result of both sabotage and negligence. Three supervisors were arrested.

The garment industry, which accounts for 80 percent of the country's $24 billion annual exports, is a mainstay of the economy along with remittances from Bangladeshis working overseas.

(Reporting by Ruma Paul; Editing by Anis Ahmed and Sanjeev Miglani)