Prime Minister David Cameron has accused campaigners for British exit from the European Union of lying to voters — but says he is not worried that the "remain" side is losing ground.

With polls giving a mixed picture, bookies' odds on an "out" vote in a June 23 referendum have been slashed from about 4-1 to as short as 2-1 in recent days.

"Leave" campaigners feel they are gaining momentum with their argument that leaving the bloc is the only way to control immigration.

Cameron, who heads the "remain" campaign, told a hastily convened press conference Tuesday that anti-EU campaigners were "resorting to total untruths to con people into taking a leap in the dark."

Asked if he was worried his side was losing, Cameron said "not at all."