Reading from a statement to open Prime Minister’s Questions, Mr Johnson acknowledged the public “rage” over the incident. but insisted he thought it could have been technically within the rules.
Mr Johnson told MPs that he attended the May 20, 2020 gathering for around 25 minutes to “thank groups of staff”.
He then he had then returned to his office to continue working.
"Mr Speaker, I want to apologise,” Mr Johnson said in a statement.
"I know that millions of people across this country have made extraordinary sacrifices over the last 18 months. I know the anguish that they have been though, unable to mourn their relatives, unable to live their lives as they want or to do the things they love.
"And I know the rage they feel with me, with the Government I lead, when they think that in Downing Street itself, the rules are not being properly followed by the people who make the rules.
"And though I cannot anticipate the conclusion of the current inquiry, I have learned enough to know there were things we simply did not get right.
"And I must take responsibility.
“No.10 is a big department with the garden as an extension of the office, which had been in constant use because there was a lot of pressure in stopping the virus and when I went into that garden just after six [o’clock] on the 20th of May, 2020 to thank groups of staff before going back into my office 25 minutes later to continue working, I believe implicity that this was a work event.
"But Mr Speaker, with hindsight I should have sent everyone back inside, I should have found some other way to thank them.
"And I should have recognised that, even if it could be said to technically fall within the guidance, there would be millions and millions of people who would simply not see it that way, people who suffered terribly, people who were forbidden from meeting loved ones at all, inside or outside, and to them and to this House I offer my heartfelt apologies.”
Labour leader Sir Keir Starmer called on the Prime Minister to resign.
“After months of deceit and deception, the pathetic spectacle of a man who has run out of road,” Sir Keir said.
“His defence … that he didn’t realise he was at a party is so ridiculous that it’s actually offensive to the British public.”
Sir Keir added: “The party’s over, Prime Minister. The only question is will the British public kick him out, will his party kick him out or will he do the decent thing and resign?”
But Mr Johnson asked for senior civil servant Sue Gray to be allowed to complete her investigation into the party “so that the full facts can be established".
SNP Westminster leader Ian Blackford also urged Mr Johnson to “do the decent thing” and resign.
He said at Prime Minister’s Questions: “The Prime Minister stands before us accused of betraying the nation’s trust, of treating the public with contempt, of breaking the laws set by his own Government.
“A former member of Her Majesty’s Armed Forces, Paul, wrote to me this morning. His father died without the love and support of his full family around them because they followed the regulations, Prime Minister.
“Paul said ‘as an ex-soldier, I know how to follow the rules but the Prime Minister has never followed any rules. He does what he wants, and he gets away with it every time’.
"The Prime Minister can’t get away with it again. Will the Prime Minister finally do the decent thing and resign or will his Tory MPs be forced to show him the door?”
Mr Johnson replied: “I want to offer my condolences to his constituent who wrote to him and just to remind him of what I’ve said earlier, and with the greatest respect to him, I think that he should wait until the inquiry has concluded.”
The Prime Minister was making his first public appearance since the leak on Monday of an email from his principal private secretary, Martin Reynolds, inviting Downing Street staff to the gathering on May 20, 2020 to “make the most of the lovely weather”.
Scottish Tories leader Douglas Ross had previously said Mr Johnson must resign if he was proven to have lied over the lockdown party held at Downing Street.
Mr Johnson had previously declined to say whether he attended the gathering, but witnesses have reported both the Prime Minister and his wife were among 30 people at the drinks.
The Prime Minister has said it is a matter for Sue Gray, the senior civil servant who is investigating a series of reported parties in Downing Street and elsewhere in Whitehall in the course of 2020 to determine what happened.
However, Conservative MPs had warned in the build-up to PMQs that such a position was simply unsustainable as Mr Johnson must know whether he was at the “socially distanced drinks” or not.