David Cameron has urged people not to vote in the EU referendum on the basis of what he said were "completely untrue" claims from the Leave campaign.
The PM dismissed warnings over an EU army, the prospects of Turkey joining and the cost of the UK's membership.
In a special edition of Question Time, he said the UK would be "a quitter" if it voted to leave.
Vote Leave said the PM "just doesn't have the answers" and that people "do not believe him any more on the EU".
The referendum on whether the UK should stay in the EU or leave takes place on Thursday.
Leave campaigners say Turkey's bid for EU membership could trigger a sharp rise in migration to the UK under free movement rules.
Asked at the question and answer session in Milton Keynes whether he would use the UK's veto to prevent Turkey joining, the PM said: "I do not think it's going to happen for decades so as far as I am concerned that question simply doesn't arrive."
He said the row over Turkish membership was "the biggest red herring in this whole EU referendum debate".
The PM said Leave's controversial claim that £350m a week is spent on EU membership "isn't true" and that a European Army - which prompted a former defence chief to switch to the Leave campaign at the weekend - was "not going to happen".
"I am sure there are arguments for leaving" he said, but added that it would be a "tragedy" if the UK voted to leave on the basis of "three things that are completely untrue".
Analysis by Tom Bateman, BBC political correspondent
The prime minister strode to the stage with what looked like a single sheet of notes - perhaps because the message he wanted to get across was succinct.
It could be summed up as "listen to the experts" because a vote to leave would be "irreversible".
He repeatedly came back to this appeal to underline the remain side's core argument that a majority of economists believed leaving the EU would harm our economy.
But - in a period when we have heard much about the importance of a robust democracy - he was repeatedly challenged by a probing and at times incredulous audience.
One audience member told him she was still confused with both sides behaving badly, before David Dimbleby suggested the word of experts may not be cutting through.
And the comparison by another questioner of the PM to a "21st century Neville Chamberlain" prompted the most impassioned moment of the evening; Mr Cameron preferred an analogy with another prime minister, Winston Churchill, who he said didn't "quit on Europe".
The PM's grilling was the second of two special editions of Question Time. Justice Secretary Michael Gove, who wants to leave the EU, faced the same 45-minute format of questioning on Wednesday night.
Mr Cameron and the government are campaigning for a vote to remain, although ministers such as Mr Gove who want to leave have been granted permission to campaign for the other side.
The PM also said the government would have to put up taxes or cut spending or risk "going back to square one" if the UK voted to leave.
And he faced repeated questions on immigration, and his previous pledge to reduce net migration to the tens of thousands.
'No silver bullet'
Leave campaigners say the free movement principle makes it impossible for the UK to control its borders.
Mr Cameron said controlling immigration had been "difficult" because "lots of people want to come to this country".
But he said there was "no silver bullet" and that leaving the EU and the single market was "not the right way to control immigration".
If the UK votes to leave, he said, "that's it, we are walking out the door, we are quitting - we are giving up on this organisation".
"I do not think Britain, at the end, is a quitter," he said.
He said Winston Churchill did not "quit on Europe" during World War Two, adding: "You can't fight if you're not in the room".
Opinion polls suggest Thursday's vote will be close, with campaigning under way again after it was suspended following the death of Labour MP Jo Cox.
At the start of the programme, Mr Cameron paid tribute to Mrs Cox, saying his "heart breaks" at her death, which prompted the referendum campaign to be suspended.
The PM said it had been a "very passionate" debate so far, with strong arguments on both sides. He criticised UKIP's recent poster featuring a long queue of migrants, saying it had been an "attempt to frighten people" but said his side had highlighted "positive" message like a growing economy.
He stood by his previous claim that the leader of so-called Islamic State would be pleased if the UK votes to leave.
The PM has refused to take part in a debate against other senior Conservatives.
Vote Leave chief executive Matthew Elliott said Mr Cameron "repeatedly refused" to say he would veto Turkish EU membership and noted that in 2010, the prime minister had said he was "angry" that the country's progress towards EU membership had been frustrated and would be the "strongest possible advocate" for Turkey joining the EU.
At the time, Mr Cameron said he wanted to "pave the road" for Turkey to join the EU, saying the country was "vital for our economy, vital for our security and vital for our diplomacy".
The campaign group also pointed out that according to the official government website, the British Embassy in Ankara has a 'dedicated team working on projects to improve Turkey's prospects of joining the EU'.
Mr Elliott added: "Cameron had no answers to people's legitimate concerns on immigration tonight and failed to set out how he would meet his manifesto pledge to bring the numbers back down to the tens of thousands while remaining in the EU. He had no answer on how we would fund the NHS to cope with higher levels of immigration.
"He has avoided speaking to the British public throughout the campaign because he knows that they do not believe him anymore on the EU."