Scotland Yard has asked civil servant Sue Gray to make "minimal reference" to the Downing Street parties it is investigating in her highly-anticipated report.
The Metropolitan Police said it had not asked for the probe to be delayed but demanded anything that could "prejudice" its inquiries be stripped out.
This means key details could be removed about events the police are examining - or the report could be delayed while the force conducts its inquiries.
Opposition MPs blasted the appearance of an "establishment stitch-up" and a "Whitehall whitewash" amid confusion about the report's publication.
Downing Street had not received the report on Friday as Boris Johnson waits for findings that could determine his political future.
The Prime Minister will spend the weekend at his Chequers retreat as he seeks to shore up his battered leadership.
Ms Gray, a top civil servant, was tasked with investigating allegations of lockdown-flouting parties in Downing Street and Whitehall during the pandemic.
Her report had been expected this week - but the timescale has been derailed after Met Police Commissioner Dame Cressida Dick announced a police probe.
In a statement, the Met Police said: "For the events the Met is investigating, we asked for minimal reference to be made in the Cabinet Office report.
"The Met did not ask for any limitations on other events in the report, or for the report to be delayed, but we have had ongoing contact with the Cabinet Office, including on the content of the report, to avoid any prejudice to our investigation."
Dame Cressida said on Tuesday that a "number of events" in Downing Street and Whitehall are being looked at by officers but the force has not said which ones.
The bombshell announcement threw a major spanner into the works, with confusion about whether the Gray report could be delayed or stripped of key details.
Ms Gray is understood to have been locked in talks with lawyers and officials about what can be included, leaving Mr Johnson in limbo for days.
Lawyer Adam Wagner, who interprets Covid regulations, tweeted: "I am not a criminal lawyer so perhaps I am missing something.
"How would a factual civil service report about events the police is investigating "prejudice" their investigation?"
SNP Westminster Leader Ian Blackford demanded the report was published "in full and undoctored".
"This UK government farce has gone on long enough. People are understandably concerned that this increasingly looks like a cover up," he said.
"The Prime Minister cannot be allowed to wriggle off the hook by using the Metropolitan Police investigation as an excuse to further delay or doctor the report.
"This cannot be another Whitewall whitewash."
Fran Hall, who lost her police officer husband to Covid-19 in October 2020, said families want answers and said the prove had "turned into a circus".
She said: "Tragically, it seems here that the Metropolitan Police have broken the trust of the public by first refusing to investigate flagrant law breaking, and now demanding any other investigation’s hide the most serious illegalities happening at Downing Street.
"It’s incredibly painful and they have let families like mine down. My husband was completely committed to justice, and he would have been appalled by this."
She added: "As we predicted, the Sue Gray investigation has turned into a circus. The reality is that it’s clear that the Prime Minister broke his own laws blatantly and regularly, whilst families across the country stuck with them and suffered greatly for doing so.
"If he had any decency he would do the right thing and resign, but that quite clearly isn’t going to happen."
Technology minister Chris Philp said the timing of the report's publication was up to Sue Gray.
He told LBC: "You will have seen, as I have seen, press speculation is it is because she's discussing with lawyers and police exactly what can and can't go in it.
"But the bottom line is, I don't know because it is a report she's compiling independently and I have no visibility of what may or may not be in it, or what her thought process is."
It comes as a bizarre row emerged over whether the PM had been surprised with a cake at a birthday gathering in Downing Street in June 2020.
Tory MP Conor Burns, a close ally, was widely mocked for claiming the PM had not broken the rules as he had been "ambushed by cake".
But he later told the Telegraph: "I'm told under some authority, indeed from him, that there actually wasn't a cake."
Downing Street has never denied that Mr Johnson was presented with a cake at the gathering in the Cabinet room, where his wife Carrie was said to have led guests in a rendition of "Happy Birthday".
Mr Johnson's premiership is hanging by a thread amid mounting Tory anger at the drip of allegations of rule-breaking parties.
Seven Tory MPs have publicly called for the PM to quit, while others are believed to be waiting for the results of Sue Gray's probe before submitting a letter of no-confidence in his leadership.
At least 54 MPs need to send a letter to Sir Graham Brady, the chair of the Tory 1922 Committee, to trigger a vote of no-confidence in the PM.
Mr Johnson would have to then win the support of half of Conservatives MPs in order to stay in No 10.
