The deadline for Downing Street officials to object to being named in Sue Gray's report on lockdown parties has passed.
The senior civil servant, who has led the investigation, is expected to publish her findings within days.
Education Secretary Nadhim Zahawi told the BBC Ms Gray had "complete control" over the details revealed.
But Labour insisted the report should be published "in full and with all accompanying evidence".
The officials set to be named as having attended or organised gatherings had until 17:00 BST on Sunday to register their objections.
Whitehall sources had told the BBC that challenges could potentially delay publication of the report.
BBC political correspondent Iain Watson said that, with no one yet known to have taken out a legal challenge, it was likely that the report would be published in the next few days.
A separate investigation by the Metropolitan Police concluded this week with a total of 126 fines being issued to 83 people, including one to Prime Minister Boris Johnson.
Ms Gray has gathered evidence including 510 images during her own investigation.
The BBC understands it is unlikely all the images will be released, although it is possible some will be published to illustrate the nature of the gatherings.
Asked on BBC One's Sunday Morning programme whether all the evidence gathered by Ms Gray would be included in her report, Mr Zahawi replied: "I would absolutely welcome it. It's the right thing to do."
He said the prime minister had his "full confidence", telling host Jo Coburn: "Sue Gray makes that decision [over what to include in her report]. Sue Gray has complete control over this."
On Friday it emerged that the prime minister and Ms Gray had met several weeks earlier over the report, although there are conflicting accounts of what was discussed.
Mr Johnson is facing calls to explain the meeting from opposition parties, who say it threatens to undermine public confidence in the investigation.
But Mr Zahawi said: "The prime minister would never interfere in the outcome of the investigation."
"The prime minister, throughout the process, has allowed Sue Gray to conduct herself independently," he added.
Downing Street said Mr Johnson had been "clear throughout" that the report should be "completely independent", and its findings had not been discussed.
There hasn't been a renewed clamour among Conservative MPs for the prime minister to go, now that police have confirmed the scale of the fines imposed on officials and politicians in Downing Street.
But Boris Johnson's long-standing critics will pore over the Sue Gray report to assess whether his initial assertion that Covid guidance and rules were followed was credible.
The devil for Mr Johnson will be in the as-yet-unseen detail of the Downing Street gatherings. If, for example, she were to provide descriptions - or even possibly, in some cases, images - of events that weren't socially distanced, that could potentially inflict more damage on the prime minister.
But if Mr Johnson, in the statement he will make to MPs when the report becomes public, can convince colleagues he was the victim of bad advice from his officials, then his next challenge will come in June.
That's when voters will get a chance to have their say in two crucial by-elections in Conservative held seats.
For Labour, shadow Treasury minister Pat McFadden told Sky News: "I've got every faith in Sue Gray's integrity and she is a civil servant of the highest integrity.
"We don't know the details of that meeting, it's not clear who called it, there's different accounts of that, so it's hard for me to say what was said there."
An interim version of Ms Gray's report, published in January, did not name individuals but criticised "failures of leadership and judgement" and said some events should not have "been allowed to take place".
The publication of her full findings was delayed when the Met Police launched its own investigation.
The prime minister faces a further inquiry by the Commons' Privileges Committee about whether he knowingly lied to Parliament when he previously told MPs that no laws had been broken in Downing Street.
Under government guidelines, ministers who knowingly mislead the House of Commons are expected to resign.