Anwar Hussin, a member of Myanmar's Rohingya ethnic group, fell ill shortly after he was detained on October 9, according to People's Forum on Burma, a Japan-based NGO headed by a Japanese lawyer.
Citing the 57-year-old's cousin, the group said Hussin had been complaining of a headache all morning and fell unconscious as he began eating lunch in his cell.
Fellow detainees, seven people of different nationalities, called for help because he was vomiting and having spasms, the NGO said.
A doctor was summoned 51 minutes after Hussin's collapse, according to a timeline given to his cousin by the centre.
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Staff made an emergency call four minutes after the doctor's arrival, 55 minutes after being made aware of the problem, the timeline showed.
Hussin died in hospital on October 14, it said.
A spokeswoman for the Tokyo Immigration Bureau said a man in his 50s from Myanmar, formerly known as Burma, died of subarachnoid haemorrhage, a stroke, after collapsing in the detention centre, confirming the dates given by the pressure group.
"We refrain from disclosing details because it concerns private matters," said the spokeswoman.
"We are aware that some people have complained the man was neglected for some time," she said, adding the bureau believes staff handled the case appropriately. She said officials had explained the situation to the man's surviving family in Japan.
The People's Forum on Burma, which supports democratisation of Myanmar and aids refugees from the country when they arrive in Japan, disputes this.