Mr Corbyn told the BBC's Andrew Marr Show he was enjoying "every moment" of his time as leader.
He has found himself at odds with some of his MPs on issues including air strikes in Syria and Trident renewal.
Unite union chief Len McCluskey accused Mr Corbyn's critics of using the Syria debate to undermine his leadership.
The Labour leader's opposition to air strikes is not shared by most of his shadow cabinet - and his decision on Thursday to write to MPs setting out his opposition provoked an angry reaction and the threat of resignations if his front bench are ordered to vote with him next week.
Meanwhile his ally, shadow chancellor John McDonnell, was criticised by some in the party for his response to George Osborne's Spending Review - during which he quoted Chairman Mao in the House of Commons.
Mr Corbyn, the Islington North MP who won the Labour leader race with more than half of the votes earlier this year, said: "I feel there are some people who haven't quite got used to the idea that the party is in a different place. It's much bigger than it's been in all of my lifetime.
"We have a very open electoral system. The result was a very, very clear mandate for me to be leader of the party.
"I'm not going anywhere. I'm enjoying every moment of it."
Andrew Marr put it to Mr Corbyn that he had had a "terrible, terrible few weeks" including suggestions by Newport West MP Paul Flynn saying the  leader may be forced to resign over his stance against air strikes in Syria as it was causing "terrible divisions" in the party.
But Mr Corbyn hit back and said: "It hasn't been terrible at all, party membership has gone up, we forced the government to retreat on tax credits, we forced the government to retreat on police cuts."
Mr Corbyn also said headlines about him being against a shoot-to-kill policy in the event of a terror attack had been "spun" in the media which was a "regret".
Seeking to clarify his position, he said: "Shooting to kill on the streets of Britain, purely based on suspicion, is illegal and dangerous.
"Involving a direct intervention by security forces, as happened in Paris, to stop someone setting off a bomb or shooting a gun directly at somebody is a reasonable form of response."
Mr McDonnell told BBC 5 Live's Pienaar's Politics that what looked liked "splits" within the party were actually democracy in action, and were "healthy" expressions of different views.
Labour MP Stephen Kinnock, meanwhile, compared Mr Corbyn to "Marmite" adding: "It's one of those where people love it or they don't."
Former shadow business secretary Chuka Umunna, himself briefly a Labour leadership contender earlier this year, told Sky News Mr Corbyn was a "good and decent man who has deeply-held beliefs", while former deputy prime minister Lord Prescott told BBC Radio 4's The World This Weekend he was concerned about party unity.
He said: "You've got to cry, haven't you? Most of our people, when I go round the country people say to me 'John, what the hell is happening?'"
In a Huffington Post article, Mr McCluskey - who recently criticised the Labour leader - said Mr Corbyn had been "denounced" for expressing his views on Syria while shadow ministers were making their pro-air strikes views clear.
He denounced backbench MPs for calling on Mr Corbyn to "quit for having the temerity to maintain his values and principles".
Mr McCluskey said Unite - Labour's biggest financial backer - would "resist all the way" any attempt to force Mr Corbyn out through a "Westminster Palace coup".
Labour's Jeremy Corbyn has insisted he is "not going anywhere", despite reports of potential leadership challenges against him from his MPs.