The Prime Minister told MPs he had ordered an investigation into the event after leaked footage showed senior No.10 aides laughing at a mock press conference about the party.
Speaking at Prime Minister’s Questions on Wednesday, Mr Johnson claimed he had no knowledge of the party happening and repeated his denial.
He said: “I understand and share the anger up and down the country at seeing No. 10 staff seeming to make light of lockdown measures, and I can understand how infuriating it must be to think that people who have been setting the rules have not been following the rules because I was also furious to see that clip.
“I apologise unreservedly for the offence that it has caused up and down the country and I apologise for the impression that it gives.
“But I repeat that I have been repeatedly assured since these allegations emerged that there was no party and that no Covid rules were broken, and that is what I have been repeatedly assured.
“I have asked the Cabinet Secretary to establish all the facts and to report back as soon as possible – and it goes without saying that if those rules were broken, then there will be disciplinary action for all those involved.”
The Prime Minister’s apology “raises more questions than answers”, Sir Keir Starmer told the Commons.
The Labour leader said: “The Prime Minister, the Government, spent the week telling the British public there was no party. All guidance was followed completely.
“Millions of people now think the Prime Minister was taking them for fools, that they were lied to. They are right, aren’t they?”
Mr Johnson replied: “I think he missed what I said. I apologise for the impression that has been given that staff in Downing Street take this less than seriously. I am sickened myself and furious.”
Sir Keir then questioned the need for an internal investigation, saying “the situation is as clear as day”.
He said: “Surely the Prime Minister hasn’t now going to start pretending that the first he knew about this was last night? Surely we have all watched the video of the Prime Minister’s staff including his personal spokesperson.
“They knew there was a party, they knew it was against the rules, they knew they couldn’t admit it, and they thought it was funny.
“It is obvious was happened. Ant and Dec are ahead of the Prime Minister on this. The Prime Minister has been caught red-handed. Why doesn’t he end the investigation right now by just admitting it?”.
Mr Johnson insisted: “Because I have been repeatedly assured that no rules were broken.
"I understand public anxiety about this, but there is a risk of doing a grave injustice to people who have frankly obeyed the rules.”
SNP Westminster leader Ian Blackford told the House of Commons that if the Prime Minister does not resign, “he must be removed”.
He said: “People across these islands have followed the rules even when it meant missing friends and family, missing births, missing funerals, missing the chance to be beside a loved one in their dying moments.
“People have sacrificed at times to the point of breaking, while the UK Government has laughed in their faces. It is clear that this Prime Minister has lost the support of the public and now even of his own benches.”
Mr Blackford noted this was a “moment of moral reckoning”, adding: “Every member of the Conservative benches must now decide – is this the man to lead these islands when lives are at stake?”
He went on: “It is time for members in this House to act. If he doesn’t resign, then he must be removed.”
Mr Johnson replied: “I thank the right honourable gentleman for his support and vote of confidence, but I can tell him I am going to get on with the job.
“I believe that is what is the right thing to do and I think it is very, very sad that when the public needs to hear clarity from their officials and politicians, the parties opposite are trying to muddy the waters about events or non-events of a year ago.”
First Minister Nicola Sturgeon urged the Prime Minister to “come clean” over the party.
“The Prime Minister appears to be not being straight and truthful about it,” Ms Sturgeon told the BBC.
“That really matters because he is likely to be asking people to do difficult things again over this Christmas and it’s really important that he’s straight and honest with people – if mistakes were made, to own them, to apologise for them.”
She added: “I think this is a really serious issue for the Prime Minister and I think he has to come clean.”