Charles Kennedy has told Liberal Democrat MPs he intends to lead them into the next election, as he fights for his political life.
Mr Kennedy addressed them at a routine meeting, which followed criticisms from inside his own "shadow cabinet".
Afterwards, Mr Kennedy said he had received "overwhelming" support from MPs who spoke at the meeting.
But in a BBC News interview, he refused to say whether deputy leader Sir Menzies Campbell had backed him.
Concerns about Mr Kennedy's performance were voiced at a meeting of the Lib Dem "shadow cabinet" on Tuesday, but nobody asked him to resign.
The BBC has learned that some frontbenchers considered writing a letter threatening to resign if Mr Kennedy did not quit as leader. But they never sent it.
BBC political editor Nick Robinson said nobody would challenge Mr Kennedy in the next few days but they could attack him again in the future.
Mr Kennedy raised the issue when he met Lib Dem MPs on Wednesday evening.
He said he was grateful to the MPs who had backed him "to the hilt", and there had been silence when people were invited to say whether they wanted a new leader.
"The overwhelming majority of the voices that were raised in our parliamentary meeting over the course of 90 minutes tonight were supportive of me personally and of my political leadership of the party," he said.
The MPs were also "very, very critical indeed of anonymous background unattributable briefings to the press", he said.
Mr Kennedy said no leader should be "immune from criticism" but the MPs who had spoken at the meeting wanted him to stay on.
Foreign affairs spokesman Sir Menzies, 64, is seen as a possible successor. He has just been given a clean bill of health after treatment for cancer.
Another potential alternative to Mr Kennedy, 46, could be party president Simon Hughes, 54.
Asked if Sir Menzies had told him he supported his leadership, Mr Kennedy said he did not disclose the details of private conversations.
Earlier, frontbencher Lembit Opik attacked Mr Kennedy's unnamed detractors.
He told BBC News 24: "Why go through the press and brief in what I think is a slightly cowardly way, rather than going directly to the boss and having a conversation with him and moving it forward?"
Mr Opik argued that Mr Kennedy had secured the best result for the party since the 1920s at May's general election, by winning 62 seats.
Former Liberal leader Lord Steel said the critics should "shut up or put up".
Treasury spokesman Chris Huhne thought Mr Kennedy would see off his critics but admitted the party needed to "raise its game".
And Lib Dem peer Lord Carlile of Berriew said a lot of senior party figures wanted - and some "craved" - strong leadership.
He told BBC News 24's Hardtalk programme Mr Kennedy had been very successful, but some people harked back to Paddy Ashdown's leadership style.
"There is a legitimate question at the present time as to whether Charles Kennedy is providing the kind of frontline leadership that the party needs in the present part of the political cycle where the Conservative party has a new dynamic, energetic leader," he added.
Former parliamentary party chairman Matthew Taylor told BBC News that Mr Kennedy had been a great leader.
But he added: "Any leader is going to contemplate their position after two general election wins with a young family, but that is a decision he will make."
At prime minister's questions on Wednesday, Conservative leader David Cameron taunted Mr Kennedy about the Lib Dems' "decapitation strategy" - a reference to the party's failed attempt to unseat senior Tories at the general election.
Labour and Conservative MPs jeered Mr Kennedy with shouts of "bye, bye Charlie".
Mr Kennedy was re-elected unopposed as party leader in June, after the general election, but faced speculation about his leadership at the autumn party conference.
Lib Dem leaders can be deposed if a no confidence motion is approved by a majority of the party's MPs. Candidates in a leadership election have to have the support of at least seven MPs.