Former Royal Mail chairman Allan Leighton has said the Horizon scandal is "unbelievable" and "terrible".
Mr Leighton apologised for "elements" of the scandal that occurred during his time in the role.
Earlier, a former Post Office investigator also apologised for not probing reported problems with the Horizon IT system, blaming cost.
But ex sub-postmaster Seema Misra, who he investigated, said apologies "don't make any difference".
Between 1999 and 2015 hundreds of sub-postmasters were wrongfully convicted of offences including theft and false accounting on the strength of faulty Post Office Horizon data.
At the time of Mr Leighton's employment there, between 2002 and 2009, the Post Office was a subsidiary of Royal Mail.
He told an inquiry into that the scandal "has been a terrible thing for everybody who has been involved in it, particularly the sub-postmasters and sub-postmistresses".
"It's unbelievable that it's happened and I just wanted to say that I'm sorry that elements of that occurred while at my tenure at the Royal Mail.
"I'm sorry for that happening."
Separately, former Post Office investigator Jon Longman said he should have tried harder to get data requested on behalf of Ms Misra, who was eight weeks pregnant when she was sentenced to 15 months in prison.
Giving evidence to an inquiry into why so many sub-postmasters had been wrongfully accused, Mr Longman said "cost should not have come into it" in granting Ms Misra's repeated requests for data.
The organisation later had a policy of limiting data requests.
Julian Blake, one of the lawyers acting for the Post Office Horizon IT inquiry, asked why the requests had been rejected.
An internal Post Office email from June 2009 argued the size of Ms Misra's request would have used up too much of its "quota", while another email argued that a lot of postmasters tend to "plead guilty at the 11th hour".
"With hindsight, I wish the data requested had been provided," Mr Longman told the inquiry, adding that he "should have been a bit more forceful in getting disclosure to the defence".
Investigators were concerned there would be a "world of trouble" if the firm lost her test case.
Speaking to the BBC at the Post Office inquiry Ms Misra said: "The apologies don't make any difference. I don't know if I'll ever accept their apologies. I can't get the time back."
She said she wanted "proper compensation for each and every victim and accountability", adding that every person who was responsible for the scandal - either in the authorities, the Post Office, Royal Mail or Fujitsu - needed to be put behind bars.