Priti Patel has been accused in parliament of seeking to block or redact an independent report into the murder of a private detective as part of a potential “cover up” to protect friends in Rupert Murdoch’s media empire.

Labour MP Chris Bryant, who secured an urgent question into the home secretary’s decision to vet the report into Daniel Morgan’s 1987 killing, said there were concerns that “people with very close friends in News International might want to delay or even prevent this publication”.

Responding to Bryant, Home Office minister Victoria Atkins insisted Patel wanted the report published as soon as possible but that she was obliged to first check it for any national security concerns.

Atkins declined to address requests from Bryant and other MPs to list any meetings or other communications between Patel and Murdoch’s newspaper grouping, now known as News UK.

No one has been convicted of the murder of Morgan, who was found in a south London car park with an axe embedded in his head. The eight-year inquiry into allegations his killers were shielded by police has been completed, and was due to be published this week.

But last week Patel said she would need to check the report before it was published. This prompted anger from both the inquiry panel and from Morgan’s family, who say it breaches the agreement made when it was set up by then home secretary Theresa May.

Bryant told the Commons that Patel had acted wrongly in seeking to review the report: “She has no power in law to do that. Her own terms of reference only allow her to make arrangements for publication for parliament.”

He asked Atkins to agree a date for publication this week “in full, without deletion, amendment or redaction”, and to list any communications Patel, her officials or an adviser had with News UK, Murdoch or News UK’s chief executive, Rebekah Brooks.

“Because people are worried that she’s not going to do that,” he said. “It’s not difficult to see why powerful people with very close friends in News International might want to delay or even prevent this publication.”

If Patel refused to act, Bryant said, “won’t people conclude that the cover-up is still going on?”

Atkins responded by saying Patel had not received the report – the panel has refused to send it if it might be redacted. The home secretary would not amend the document, Atkins said, with “the only caveat” being national security and the Human Rights Act.

Nick Thomas-Symonds, the shadow home secretary, called the delay a “kick in the teeth” for Morgan’s family, and said that the terms of reference limited Patel’s role to receiving the report, putting it before parliament and responding to it.

A Metropolitan police team had already carried out a security check on the finished report, he added.

Atkins replied that Patel, as home secretary, “has her own responsibilities that she cannot transfer to anybody else” in terms of national security.

The SNP’s Stuart C McDonald also pressed Atkins to disclose any links or communications between Patel or her officials and News UK. Atkins again ignored the subject in her reply.

Patel attended Murdoch’s 2016 wedding to Jerry Hall. The Home Office has said she will not discuss her relationship with Murdoch as it is a private matter.

Writing for the Guardian on Saturday, Morgan’s son, also called Daniel, condemned the plan to vet the report, saying this was never part of the inquiry process, and that Patel’s actions had exacerbated the family’s ongoing “living nightmare”.