In a personal letter to the family of Alton Manning, Richard Tilt will apologise for his comments that physical differences meant that black people were more likely than whites to suffocate while being restrained by prison officers.
Mr Tilt made the comments in response to questioning by Jeremy Paxman on BBC Newsnight, and was forced to row back from the statement in the face of an angry reaction from penal reform and ethnic minority rights campaigners.
His position was made more difficult after health experts stated that there was no medical evidence to back his claim.
He has already issued a statement saying he "was greatly concerned at any upset his comments may inadvertently have caused" after a jury decided Mr Manning was unlawfully killed at the privately-run Blakenhurst prison, Worcestershire.
But a spokesman for the family said the personal apology from Mr Tilt was not enough and called for his resignation. Maxie Hayles, the co-ordinator of the Alton Manning Justice Campaign, said the family did not want to hear from Mr Tilt.
"As far as I'm concerned his apology comes a bit late, after the damage has been done," he said.
"Ideally we would like his resignation, not this wishy-washy apology. His comments were premeditated and well thought-out before he said them."
Mr Manning, 33, of Sparkbrook, Birmingham, died after being restrained during a struggle. Seven prison officers were suspended following the inquest verdict.
A Prison Service spokesman said that Mr Tilt would be apologising for any offence caused by his remarks.
"He will tell them there was no offence intended and he is certainly not a racist.
``He will express regret for the death of Alton Manning," he added.