Pressure has been building on Clegg since the Lib Dems lost 11 of their 12 European Parliament seats, which came hot on the heels of the party losing hundreds of seats in local council elections.
Emerging for his first public appearance since the vote debacle, Clegg said during a low-key visit to a youth club that he wanted to "finish the job" and dismissed calls to dissolve the coalition or modify his party's pro-EU approach.
One new poll showed Clegg could even lose his own seat in next year's election to the centre-left main opposition Labour Party.
Clegg received backing from Conservative Prime Minister David Cameron, with Downing Street making clear he wanted him to remain as his deputy.
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While senior Lib Dems have publicly pledged support, a number of his party's lawmakers and activists have warned he is "toxic" for voters and must go.
Clegg said: "I admit it has been a massive setback for us last week but we were right to stick to our values and right to seek to make that case because no one else was doing it and no one else is doing it in British politics."
Former prime minister Tony Blair, who won three elections for the Labour Party, said he admired the "leadership and courage" the Lib Dem leader had shown in office.