Former Brexit secretary David Davis has called for Neil Basu to be pulled from an investigation into the leaking of cables from Britain's US ambassador Sir Kim Darroch.
The Metropolitan Police was accused of being "heavy-handed" after it announced a criminal probe into the leaking of the cables, adding that any further release could be a "criminal matter".
Mr Basu, assistant commissioner at Scotland Yard, urged journalists in possession of leaked Government documents to return them, warning any further publication from the dispatches cables could result in prosecution.
Mr Davis wrote to the Times accusing Mr Basu of "straying beyond his brief" and called for commissioner Cressida Dick to put the investigation in the hands of "an officer who puts preservation of our free press ahead of protection of the state's reputation".
He wrote that prosecuting journalists for "embarrassing the state is not what we do in the UK".
He added: "Furthermore, while I deplore the release of diplomatic telegrams, it is seriously debatable whether this is a criminal act.
"If so, why did the Foreign Office not engage the DA notice procedure on being notified of the leak, and prevent publication?"
Mr Davis also urged people to "get a sense of balance... into this annoying, by essentially temporary, diplomatic spat".
Meanwhile, the chairman of the Digital, Culture, Media and Sport committee Damian Collins urged the force to focus on the leaker, rather than the media publishing the leaks.
He told the Sun: "The Metropolitan Police should... make it clear that there is no legal risk for newspapers freely reporting on the leaked documents.
"Neil Basu's statement was clearly a threat aimed at newspaper editors encouraging them not to report on a story, in which there is clear public interest.
"This was wrong. If an offence has been committed, it is by the leaker and the police investigation should focus on that.
Sir Kim resigned last week saying his position had become "impossible" following the leak of diplomatic cables in which he described Donald Trump's White House as "inept" and "dysfunctional".
The Mail on Sunday released details of a memorandum from May 2018 in which the ambassador suggested Mr Trump had decided to pull out of the Iran nuclear deal in an act of spite because it was agreed by his predecessor Barack Obama.
He wrote: "On the substance, the administration is set upon an act of diplomatic vandalism, seemingly for ideological and personality reasons – it was Obama's deal."
Meanwhile, Foreign Secretary Jeremy Hunt has indicated Britain's next ambassador to the United States should be a career diplomat from within the ranks of the Foreign Office.
Following the resignation of Sir Kim, there has been speculation Boris Johnson would seek to appoint a political figure who could get close to the Trump administration if he succeeds in becoming prime minister.
However Mr Hunt, his rival for the Tory crown, said there were some "outstanding candidates" from within the Diplomatic Service for the plum Washington posting.
"I think that one of the best things about our diplomatic service are the skills acquired over very many years by career diplomats and Sir Kim Darroch exemplified that," he told BBC Radio 4's Broadcasting House.
"We have some outstanding candidates who do have that experience, and we will obviously look at them."