Shadow health secretary Andy Burnham denied ordering a "cover up" of hospital failings and accused Jeremy Hunt of launching a "smear campaign without evidence" against him.
Emails released under freedom of information laws showed the Department of Health under Labour tried to stop details emerging of a hospital scandal involving higher-than-normal death rates.
Mr Burnham - who was health secretary at the time - was recorded as being "furious" when news leaked of poor standards of care in November 2009, months before the general election.
Mr Hunt, who now holds the post in the coalition Government, seized on the emails as "s hocking revelations on Andy Burnham's attempts to cover up failing hospitals".
"We're legislating to make sure this can never happen again," he wrote on Twitter.
But Mr Burnham insisted they showed only that he was concerned that disclosure rules had been broken and challenged Mr Hunt to substantiate his claims or apologise.
"It is impossible to see how you can claim this mounted to a cover-up," he told him in a letter.
"I therefore ask you, by the end of today, to provide me with evidence to substantiate your assertion.
"If you fail to provide such evidence, I will require a full retraction and public apology. If that is not forthcoming I will consider further action."
The emails, released by the Care Quality Commission (CQC) watchdog following a request by Tory MP Steve Barclay, relate to Basildon and Thurrock University Hospitals NHS Foundation Trust.
They showed the DoH ordered the CQC not to brief the press on an inspector's report into the trust, which found appalling standards of hygiene.
But by then the CQC had already told three national newspapers the report was impending and the story was being published by the Press Association.
The CQC report into Basildon detailed major concerns about unusually high death rate among patients.
Inspectors found blood stains on floors and curtains, blood splattered on trays used to carry equipment and badly soiled mattresses in the A&E department with stains soaked through.
They also found equipment being used repeatedly that should only be used once and resuscitation room equipment that was past its use-by date.
The CQC "arguably sat on a highly sensitive safety issue for six months before informing patients and the public", according to the emails from senior CQC staff to DoH officials. They added: "Defending material which is not defensible is always a bad place to be."
Mr Barclay, MP for North East Cambridgeshire, said Mr Burnham's position as shadow health secretary was "untenable"as he was shown " putting pressure on the regulator to water down its concerns".
But Mr Burnham insisted the emails showed only that "my concern stemmed from the fact that CQC/DH rules had been broken.
"Further, the note records that I ordered a press release, in accordance with proper process, be issued later that day."
A Labour spokesman said: " It is high time he (Mr Hunt) focused on his real job and the unfolding A&E crisis instead of orchestrating a smear campaign without evidence."