Jacob Rees-Mogg has said there will not be a hard border on the island of Ireland, even in a no-deal scenario.
The chairman of the European Research Group said there may be changes but there would "not be a hard border".
The Conservative MP's pledge came as Ireland's Europe Minister insisted her government would "absolutely not" renegotiate the backstop.
Helen McEntee told BBC Radio 4 on Friday the border was not just about "customs, economy and trade".
Mr Rees-Mogg, who opposes the backstop, was in Northern Ireland on Thursday for a DUP fundraiser in Ballymena.
"The Common Travel Area will remain, so people will be able to go freely across the border between Northern Ireland and the Republic of Ireland, and there is no desire from anybody to erect physical barriers," said Mr Rees-Mogg.
"But there may be changes because we are after all leaving the European Union, the Customs Union and the Single Market."
The Common Travel Area was established in 1923 and gives UK and Irish citizens certain reciprocal rights in each others' countries, which mostly relate to unrestricted travel between each jurisdiction.
The UK and EU have agreed it will continue to operate after Brexit.
Speaking to BBC Radio 4 on Friday morning, Irish Europe Minister Helen McEntee said it was "not a normal border".
"It is over 500km long, it has 208 plus crossings and goes through peoples' farms, the back of their homes, communities," she said.
"This is not just about customs, and this again we have to remind people, it is not about economy and trade, which is extremely important to this, to the all island economy.
"This is about protecting a peace process, this is peoples' memories and what they have gone through in the past and no amount of technology can address that."
On Tuesday, MPs in Westminster voted in favour of the UK seeking changes to the withdrawal deal, by backing an amendment that called for "alternative arrangements" to the backstop.
Although it is not binding, Prime Minister Theresa May said it gave her a mandate to return to the EU and ask them to re-open the Brexit deal.
So far, the EU and the Irish government have said there can be no renegotiation of the backstop - the insurance policy in the Brexit deal to avoid a hard border.
Ms McEntee reiterated that position.
"This is a deal that took two years to negotiate. It is not for reopening," she said.
"We have had all of these discussions. We are not at the beginning of negotiations, we are at the end."
Mr Rees-Mogg had said he believed the EU would engage on the backstop if the UK came forward with "a serious set of new proposals".
"They will want to consider them seriously," he said.
"Because the alternative is the EU don't get £39bn, the trade particularly and potentially from the Republic of Ireland could face very high tariffs and that would be damaging to European economic interests."