David Cameron: Brexit will leave UK at greater risk from terrorism
The Prime Minister spoke out amid claims thousands of asylum seekers could arrive in Kent "overnight" if Britain votes to quit the EU.
At the moment, an agreement between the French and UK governments means British border guards are allowed to conduct passport checks in France.
But Mr Cameron refused to deny suggestions that it could collapse in the event of a Brexit - and went further by claiming that could put the UK's national security at risk.
He also challenged those who back Brexit to set out their vision of how Britain would look outside the EU, as he all-but confirmed he will campaign to stay in.
"There are any number of opposition politicians in France who would like to tear up the excellent agreement we have with France to make sure we have our birders on their side of the Channel. I don't think we should give those politicians any excuse to do that," the Prime Minister said.
"This is a bilateral agreement, it's a good agreement. It means that our borders are effectively in Calais, not in Dover. That is good for Britain. I want to keep that."
He added: "If we stay in a reformed EU, you know what you get - a border in Calais and vital information about criminals and terrorists running around Europe.
"The people who want to take a different path need to start answering some questions about what it would look like. They fear that, and the time will come pretty soon when they have to start answering some of those questions."
Earlier, a spokesman for the Prime Minister said: "The point being made is that should we leave the EU, some of these other arrangements we have in place with other countries, such as France, could be called into question. If they are, then we have potentially thousands of asylum seekers currently cooped up in northern France who could come here overnight.
“This is a perfectly feasible scenario that could happen."
But Eurosceptics, including many senior Conservatives, reacted angrily to the claims, with some claiming it had echoes of the campaign to keep Scotland in the UK, which was dubbed 'Project Fear'.
Former Defence Secretary Liam Fox said he was disappointed that the Prime Minister had "stooped to this level of scaremongering".
David Davis, who was beaten to the Tory leadership by Mr Cameron, said: “As the argument slips away from the Remain campaign they are forced to rely on desperate scaremongering."
Vote Leave chief executive Matthew Elliott said: "UK border controls are in France because of a bilateral treaty, not because of our EU membership, and a result of the camps in Calais, not the cause of them.
"Clearly, No 10 is in a blind panic over the failing renegotiation."