Tony Blair has said he finds it "absolutely extraordinary" that many unionists in Northern Ireland support Brexit, given its potential consequences for the region's political settlement.
The former prime minister said the emergence of a hard border between Northern Ireland and the Republic of Ireland would undermine one of the key planks of the Good Friday Agreement.
He reiterated his warning that a return of border checks on the 310-mile frontier could pose a risk to the peace process.
Mr Blair said the Good Friday deal had worked because it gave both unionists and nationalists key concessions.
He said unionists secured the principle of consent - ensuring the future of Northern Ireland's place within the UK could only be changed with the support of the region's electorate - while nationalists obtained legitimacy for their aspirations for a united Ireland.
The former Labour leader said Brexit could undermine the latter, if it was accompanied by any measures that would undermine the current free-flowing, open border.
That, he said, would skew the balance of the deal that has brought a measure of stability around Northern Ireland's constitutional position.
"If I was a unionist in Northern Ireland I would be very worried about this," he told the Press Association.
"That is why I find it absolutely extraordinary that you have got significant parts of unionism that are pro-Brexit because it's bound to cause a problem.
"I am not saying the problem can't be overcome and it's going to have to be overcome if we do Brexit."
The thorny issue of the Irish border remains a key sticking point in the Brexit negotiations.
Talks between the UK and EU are focused on the conundrum of maintaining free movement across the frontier if the UK operates a different customs regime post-Brexit.
Mr Blair, a high-profile opponent of the UK's exit from the European Union, insisted he was not using the Irish problem to forward an agenda.
"This is not an invention," he said.
Mr Blair said he could see why unionists would be opposed to any solution that would see Northern Ireland adhere to different customs rules to the rest of the UK.
But he added: "Because what unionism got from the Good Friday Agreement was acceptance of the principle of consent, it's really important in those circumstances that the other side of the bargain - namely the acceptance of the nationalism aspiration - is kept intact.
"The problem with Brexit is it leads to a situation where over time the UK is going to go in their direction and the Republic, because it is part of Europe, is going to go in the other direction and of course it's going to cause strain."
Asked if Brexit had the potential to threaten the peace, Mr Blair said: "If you end up with a hard border then it's a big problem."