Cameron, who is campaigning for Britain to stay in the union, accused the Leave campaign of alienating British Muslims and claimed the warnings were a "sign of desperation".
Campaigners for a Brexit vote on June 23 have repeatedly raised the spectre of millions of Turks being free to live in Britain as a reason to pull out of the 28-nation bloc.
There are currently about 500,000 people of Turkish origin living in Britain, according to the Home Office.
"I do find it concerning the way that the Leave campaign are talking about Turkish people in this referendum," Cameron told online newspaper Muslim News.
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"Some of the material they are putting out, painting Turkish people as criminals or terrorists, is frankly appalling," he added.
"Many British Muslims will be offended by the way they are trying to frighten people. I think it's a sign of desperation."
The Leave camp is currently lagging in the polls, with bookmakers heavily favouring Britain's continued membership of the EU.
It also put out a video warning that "David Cameron cannot be trusted on Turkey", alongside footage of lawmakers fighting in the Turkish parliament, and a crude map with arrows pointing from Turkey to Britain.
Immigration has been a key issue during the debate, with Leave campaigners warning that a Brexit was the only way to end mass migration from within the bloc.
Shortly after he took office in 2010, Prime Minister David Cameron visited Ankara to make the case for Turkish membership of the EU, saying he would "remain your strongest possible advocate".
But in an appearance before a parliamentary committee earlier this month, Cameron said that Turkish membership was not "remotely on the cards -- I don't think it will happen for decades".
After applying in 1987, Turkey began EU accession talks in 2005.
"At the current rate of progress, they'd probably get round to joining in about the year 3000," he added.