Turkey is on course to join the European Union in the year 3000 on its current rate of progress, David Cameron said, as he launched a brutal attack one of his own ministers.
The Prime Minister attacked Penny Mordaunt's claims that Britain had no veto over Turkish accession to the 28-member bloc as "misleading" and "absolutely wrong".
Turkey is set to join the EU in the next eight years and the UK will be unable to block the move, the Armed Forces Minister had insisted.
But Mr Cameron told ITV's Peston on Sunday: "The Leave campaign are making a very misleading claim."
Asked if Ms Mordaunt had been wrong to say Britain would not be able to veto its membership, he replied: "Absolutely wrong. Let me be clear, Britain and every other country in the European Union has a veto on another country joining. That is a fact, and the fact that the Leave campaign are getting things as straightforward as this wrong should call in to question their whole judgment in making the bigger argument about leaving the EU."
Pressed on whether she was qualified to remain in government, the prime minister told the programme: "Her responsibilities are in the Ministry of Defence, she is doing a very good job.
"But on this question of whether of not we have a veto, the Leave campaign are wrong."
Mr Cameron added: "It is not remotely on the cards that Turkey is going to join the EU any time soon. They applied in 1987. At the current rate of progress they will probably get round to joining in about the year 3000 according to the latest forecasts."
As the increasingly bitter clashes between the Remain and Leave camps fuelled divisions within the Conservatives, Mr Cameron insisted the party would "come back together".
"Of course this issue raises great passions. It is not surprising that you have people in a political party on either sides of the arguments," he said.
"I'm absolutely convinced that at the end of this the Government, the Conservative Party, will come back together and get on with the important job of running the country."
Asked if Boris Johnson's comparison between Adolf Hitler and the EU had made it impossible to give him a job in government, the Prime Minister told the programme: "I'm not going to get into jobs and the future now."
"Boris is hugely capable in lots of ways but I'm not going to go into Boris today," he added.
Mr Cameron insisted that he plans to serve a "full second term" in No 10.
Asked if that means he plans to stay in his post until 2019, he said: "It means a full second term, it means what it says."
The premier sidestepped questions about Chancellor George Osborne's chances of succeeding him, telling the programme: "I think he's a man of great talent.
"I'm not going to pick my, luckily I don't have to, pick my successor, the Conservative Party will do that.
"But George is hugely talented, he's a brilliant Chancellor of the Exchequer.
"You can see it in the economy; 2.5.million more people in work, almost a million more businesses since he and I got our jobs, the economy growing and so I think he's a great talent."
He added: "I think in politics you have to have partnerships. Prime ministers do not do these jobs on their own."