"It is not remotely on the cards that Turkey is going to join the EU at any time soon," Cameron told ITV television.

"They applied in 1987. At the current rate of progress, they'd probably get round to joining in about the year 3000."

Cameron wants Britain to stay in the EU.

With a month to go to the June 23 referendum, the "Remain" camp is on 55 percent and the "Leave" campaign on 45 percent, according to the What UK Thinks website's average of the last six opinion polls.

"The Leave campaign are making a very misleading claim about Turkey. Turkey is not going to join," Cameron said.

"They're basically saying vote to get out of Europe because of this issue of Turkey that we can't stop joining the EU. That is not true.

"Britain and every other country in the European Union has a veto on another country joining.

"At the current rate of progress, it would be decades, literally decades, before this even had a prospect of happening," he said of Turkish accession.

"Even at that stage, we would be able to say no."

Writing in the Sunday Express newspaper, Nigel Farage, leader of the anti-EU, anti-mass immigration UK Independence Party, said that to stay in the EU "would mean not just net migration at the current record high levels, but at rates even higher" in future if Turkey joined.

"Open borders with Turkey would be a total disaster for our country," the leading Brexit campaigner wrote.

"With a population of 80 million, it would mean even more uncontrolled migration into the UK."

After applying in 1987, Turkey began EU accession talks in 2005.

In 2010, Cameron went to Ankara to "make the case for Turkey's membership of the EU. And to fight for it".

During former Turkish president Abdullah Gul's state visit in 2011, Cameron reassured him that Britain remained strongly supportive of Turkey's EU membership bid.