Jeremy Corbyn has insisted he will "finish the job" as Labour leader and "turn back the Tory tide" despite the party's humiliating Copeland by-election defeat.
Mr Corbyn acknowledged he has not "done enough" to rebuild voters' trust in Labour but made clear he will continue despite warnings that the party is heading for a "catastrophic" general election defeat.
But he also took a fresh blow as an opinion poll showed more than a third of Labour voters (34%) were more likely to vote for the party if he was replaced as leader.
The ComRes/Sunday Mirror poll was commissioned on Friday after the Conservatives snatched the Cumbrian seat of Copeland, which had been held by Labour since 1935.
Tory Trudy Harrison's victory was also the first time a governing party had gained a seat in a parliamentary by-election since 1982.
But Mr Corbyn pointed to his thumping Labour leadership election victory in September, the second in the space of a year, as he vowed to continue.
Writing in the Sunday Mirror, he said: "We haven't done enough yet to rebuild trust with people who have been ripped off and sold out for decades and don't feel Labour represents them.
"But if we stand together, I am confident we can do that and turn back the Tory tide.
"I was re-elected Labour leader five months ago with a bigger majority and I am determined to finish that job: to reconnect Labour with our working class voters and values so we can win power to rebuild and transform Britain, for the many, not just the few."
Mr Corbyn acknowledged the Copeland result was "deeply disappointing" and took some responsibility, but blamed "globalisation" for a wider situation that he said vindicated Labour's stance not to block or delay Brexit.
"Labour's share of the vote in Copeland has been falling for 20 years and of course I take my share of responsibility," he wrote.
"Both these areas, like many others in Britain, have been left behind by globalisation and lost out from a rigged economy.
"So it's no surprise that they rejected the status quo by voting to leave in the EU referendum.
"That's why it was important for Labour to respect the result and vote for Article 50 (to trigger Brexit)."
He again pointed to the party's simultaneous victory in Stoke-on-Trent Central, where it saw off the challenge of Ukip leader Paul Nuttall, as proof it can triumph over "hate and division".
The Labour leader also vowed to attack the Tories' "endless austerity" in next month's Budget, predicting fresh spending cuts, to end a tax system "rigged for the richest", and to "fight for a positive future" after Brexit.
"We must take our message of economic renewal and fairness to every part of Britain and show that Labour has changed under my leadership," he wrote.
Meanwhile, the opinion poll also suggested that more than half (51%) of Labour voters would back the party whether Mr Corbyn is in post or not, but that nearly a third of the wider British public (31%) would prefer him gone.
A further three in five (62%) Britons do not think Labour has the right leader to win the next general election, and when Labour voters are discounted this rises to more than three quarters (77%).
More than half (59%) think Labour has lost touch with the working class and nearly half (47%) of Liberal Democrat voters would back Labour if London mayor Sadiq Khan were leader.
It comes after Labour deputy leader Tom Watson told Scottish Labour's conference in Perth that now is not the time to replace Mr Corbyn.
"All of us with leadership roles in the Labour Party need to have a long, hard look at ourselves and what's not working," Mr Watson said.
"Seven years into a Tory Government, we shouldn't be facing questions about whether we can retain the seats we already hold.
"Our job at the next election is to gain over 100 seats. Keeping what we have is supposed to be the easy bit."
He went on: "I've said it a lot recently. This is not the time for a leadership election. That issue was settled last year.
"But we have to do better. We cannot sustain this level of distance from the electorate, from our natural supporters."