Jeremy Corbyn is coming under pressure to resign after Labour lost the Copeland by-election to the Tories.
Labour had held the seat since 1935, and Thursday night's defeat is the first time an opposition have lost to a governing party in a by-election since 1982.
His own MPs warned him that Labour face a "catastrophic" general election defeat, unless he steps down.
The Labour leader admitted the result had been "very disappointing" but made clear that he was determined to carry on.
"I was elected to lead this party. I am proud to lead this party," he told reporters.
"We will continue our campaigning work on the NHS, on social care, on housing."
Fielding questions following his speech, Corbyn was asked whether he had this morning "looked in the mirror and asked yourself the question: 'Could the problem actually be me?'"
The Labour leader replied simply: "No."
Asked why not, he said only: "Thank you for your question."
John Woodcock, the MP Barrow-in-Furness, which neighbours Copeland, said the party was not an effective opposition and had to do better.
"There are always excuses you can make. But we are in trouble as a party," he told the BBC Radio 4 Today programme.
"We are on course to a historic and catastrophic defeat and that will have very serious consequences for all of the communities that we represent."
Senior Labour backbencher David Winnick said it had been a "disastrous" result: "The party is faced with the problem of a leader who is simply not acceptable to a large number of people who would normally vote Labour. That it is an obstacle and it would be wrong not to recognise that," he told the Press Association.
"It is now entirely up to Jeremy and those close to him to decide what is best in the interests not simply of the party but the people we are in politics to represent."
On a tumultuous night, Tory winner Trudy Harrison polled 13,748 votes to 11,601 for Labour's Gillian Troughton, increasing the Conservative vote share by more than 8 per cent as Labour's dropped by nearly 5 per cent.
Shadow chancellor John McDonnell, one of Mr Corbyn's closest allies, said there had been "unique" factors in Copeland which is heavily dependent on the Sellafield nuclear facility.
"Jeremy has a sense of duty. He will lead this party. He will rebuild it as a social movement, as we are doing now, and on that basis we will win the next election and he will be the prime minister," he told the Press Association.
He also hit out at Tony Blair and Lord Mandelson for high-profile interventions in the days before the by-elections.
"We can't have a circumstance again where a week before the by-election a former leader of our party attacks the party itself," he told the Today programme.
There was some consolation for Labour in Stoke-on-Trent Central, where they saw off a concerted challenge from Ukip leader Paul Nuttall.
Though that victory likely had more to do with Nuttall's disastrous campaign, with claims he had "lost close personal friends at Hillsborough" being exposed as lies.
On paper, it should have been an easy Ukip victory, with the Stoke Central overwhelmingly backing Brexit.
After Gareth Snell held the seat for Labour with 7,853 votes to Mr Nuttall's 5,233, Ukip chairman Paul Oakden acknowledged it could take years before they manage to win a seat in Westminster.
"Politics is a long game. It took us 23-odd years to win a referendum to get Britain out of the European Union," he told the BBC Radio 4 Today programme.
"It may take that long for us to get a seat in Westminster via a by-election. But if that's how long it takes then that's what we will keep doing, because that's what we are here for."
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