The Brexit secretary, Dominic Raab, has dismissed claims Theresa May could call a snap general election in the autumn to save her Brexit plans as he played down the chances of the government pivoting towards a Canada-style free trade deal.

The cabinet minister said it was “for the birds” to suggest the prime minister could go to the country after Brussels rejected her Chequers proposals at a summit in Salzburg last week. “It’s not going to happen,” he said on Sunday.

Raab insisted the government would keep negotiating with the EU on the basis of Chequers. “This is a bump in the road. We will hold our nerve, we will keep our cool and we will keep negotiating in good faith. I think we need to keep these negotiations going,” he said.

EU officials are understood to be working on a counter-proposal to Chequers, which is likely to appear in early October – after the Conservative party conference and a week before a make-or-break summit in Brussels.

However, Raab told the BBC’s Andrew Marr Show: “What we are not going to do is be dictated to. The UK is one of the biggest economies in Europe, if not in the world. We have come up with a serious set of proposals … We are not just going to flit from plan to plan like some sort of diplomatic butterfly. We are going to be resolute about this.”

The Brexit secretary also played down suggestions, raised by Jeremy Hunt on Saturday, that the government was pivoting away from its existing plans towards a free trade deal, as demanded by the Eurosceptic wing of the Tory party.

The foreign secretary had signalled that the UK could now accept a Canada-style agreement, called for by leading Brexiters including Boris Johnson and David Davis. “I am not dismissing anything,” Hunt said.

Raab, however, said such a proposal was “off the table” as it would mean reverting to the EU’s backstop solution to Northern Ireland which would create a hard border down the Irish sea.

“People need to read the small print of the EU proposals. They’re suggesting not just a free trade deal but for Northern Ireland to stay locked into … the customs union. Now that would be a clear carving of the United Kingdom,” Raab said.

“It’s off the table in the terms that the EU would even plausibly at this stage accept because it involves staying in a backstop arrangement for Northern Ireland which would leave a part of the United Kingdom subject to a wholly different economic regime. That can’t be right.”