Britons could need a visa “or some other kind of check” to travel to continental Europe after Brexit, the justice minister and leading leave campaigner Dominic Raab has said.

Raab said the issue would be a matter for post-withdrawal negotiations with the EU, but could not be ruled out if Britain wanted more secure borders.

“I think we’d have to look at that as part of the negotiations in detail. But look, at the moment president Barack Obama’s administration … is looking at new visa requirements and screening from Germany, Belgium, Greece, France, because of the recent terrorist attacks.

“I think we should at least have the power and the control to do that and make sure we keep Britain safe,” the minister told BBC1’s Sunday Politics show.

Pressed if this would mean British citizens would need visas to go to France or Germany, Raab said: “Or some other kind of check.”

He said Britain did not have enough powers to turn away EU citizens, because only 6,000 had been refused entry since 2010, compared with 67,000 people from the rest of the world.

“There are two issues here. There’s the numbers, and, as the home secretary conceded, we can’t control the numbers because of free movement if we’re inside the EU, and that makes life a lot harder. I think we can agree that’s settled.

“The second question is border, checks at the border preventative checks. Now, under UK law, with non-EU countries we can stop someone coming in because it’s not conducive to the public good. With people coming from the EU we can only deny entry if there’s a serious, credible and present threat,” Raab said.

He also said Obama had softened his stance on a trade deal with a post-Brexit Britain.

“I think what was most interesting is how far he has backtracked since Friday evening. We were told then that we were going to be sent to the back of the queue if we didn’t take his advice and stay in the EU, whereas actually what he now has said is if Britain was independent from the EU we couldn’t expect to do a free trade deal quicker than the Europeans and we couldn’t expect them to abandon the free trade negotiations with the Europeans.

“Well, no one’s really expecting that, so I think the reality of what he said is, yes, these things can take time, it has taken almost 40 years even to get to this stage, with a stalled US-EU deal. Britain can quite easily negotiate a free trade deal.”

Owen Paterson. Photograph: Dominic Lipinski/PA

The former cabinet minister Owen Paterson will say in a speech on Monday that Britain will be reduced to a colony of Brussels if it remains in the EU.

“To remain is a leap in the dark because it is a commitment to an undefined relationship with a completely new country, or leave – the safe option – where we can try to re-establish, in an orderly manner, a new relationship with our European neighbours based on trade and cooperation,” he is set to say.

“In other words, the prime minister’s ‘special status’ for countries outside the eurozone will leave Britain as a colony of Europe if we vote to remain, with the prime minister reduced to [being] a Roman governor handing down diktats from what José Manuel Barroso, a former president of the European commission, described as the ‘empire’.

“Under this scenario the notional head of the UK government would be occasionally obliged to placate the natives with the pretence of independence, while in reality [being] powerless over decisions made hundreds of miles away.”