Major and Blair say an EU exit could split the UK
Sir John Major and Tony Blair warned a vote to leave the EU will "jeopardise the unity" of the UK as they campaigned together in Northern Ireland.
They suggested a Leave vote may re-open Scotland's independence issue and put Northern Ireland's "future at risk" by threatening its current stability.
But Northern Ireland Secretary Theresa Villiers said support for the peace process there was "rock solid".
She said it would be "highly irresponsible" to suggest otherwise.
Northern Ireland first minister and DUP leader Arlene Foster said she found the intervention "rather sad".
She told journalists "I do find it rather disgraceful for two prime ministers who know full well the importance of the peace process here in Northern Ireland to come over here and suggest that a vote in a particular direction is going to undermine that".
Elsewhere in the EU referendum debate:
- The boss of JCB has written to 6,500 UK staff saying he backs a vote to leave the EU
- The government unveiled legislation to extend the voter registration deadline - as a Leave campaigner threatens legal action
- Conservative MP Sarah Wollaston has switched from Leave to Remain over claims about extra cash for the NHS
The former Conservative and Labour prime ministers, who were instrumental in the Northern Ireland peace process in the 1990s, hit the campaign trail there as Remain campaigners attempted to make the future of the UK a key question in the 23 June referendum on EU membership.
It was a message echoed by former US president Bill Clinton in an article for the New Statesman, who said he worried for Northern Ireland's "future prosperity and peace" if the UK votes to leave.
Chancellor George Osborne will travel to Scotland amid warnings that if the UK voted to leave the EU, but Scotland opted to stay in, it could trigger another referendum on Scotland's future in the UK.
Leave-supporting Conservatives have attacked the claims - saying they buy into the SNP's "bogus narrative" on separation.
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But in a joint appearance, Sir John and Mr Blair - former political rivals who led the country between 1990 and 1997 and 1997 and 2007 respectively - warned that the "unity of the UK itself is on the ballot paper" in two weeks time.
Sir John said there was a "serious risk" of another independence referendum and, if Scotland found itself out of the EU, he could "envisage a different result" to the one in 2014.
He argued that a vote to leave the EU would also risk "destabilising the complicated and multi-layered constitutional settlement that underpins the present stability in Northern Ireland" - a situation that in his words would be a "historic mistake".
He said: "It would throw all the pieces of the constitutional jigsaw up into the air again, and no-one could be certain where they would land."
Ireland would be "on the other side of the table" to Britain in its post Brexit negotiations, he added.
Mr Blair said Northern Ireland's prosperity and its political arrangements could be negatively affected by a vote to leave.
Leave campaigners say the free travel area between Ireland and the UK would be retained - but Mr Blair said this would be "difficult if not impossible" because checks would either be needed across the border between the two countries.
Otherwise, he said: "It would make a nonsense of their entire argument for leaving which is all to do with the free movement of people in the European Union."
Analysis: Sarah Smith, BBC Scotland editor
If Scotland votes one way on 23 June and the rest of UK votes another way - if as Sturgeon puts it "Scotland is dragged out of the EU against its wishes" that will undoubtedly provoke fury among many Scottish voters.
Nationalist politicians will claim that Scotland is once again being dictated to by England. And there are many eager campaigners in Scotland who desperately want the chance to vote again on the independence question as soon as possible.
But the SNP leadership are not so eager to rush into another referendum. Many senior figures in the party warn that Brexit will throw up some additional issues they don't yet have answers for.
"We understand that, although today Northern Ireland is more stable and more prosperous than ever, that stability is poised on carefully constructed foundations," he said. "And so we are naturally concerned at the prospect of anything that could put those foundations at risk."
But Ms Villiers, who backs the Leave campaign, said Northern Ireland would thrive outside the EU and the former leaders' warnings rang hollow.
"Support for the peace process in Northern Ireland is rock solid," she said.
"The vast majority of people in Northern Ireland believe their future should only ever be determined by democracy and consent and not by violence. I very much hope figures who played such an important role in the peace process would not suggest that a Brexit vote would weaken that resolve in any way.
"Whatever the result of the referendum, Northern Ireland is not going back to the troubles of its past and to suggest otherwise would be highly irresponsible."
Vote Leave has said Irish citizens would still be able to travel freely to and from the UK in the event of it leaving the EU, even though there would be controls on all other EU citizens coming into the UK once the UK was no longer bound by EU-wide freedom of movement rules.
Remain campaigners have questioned the future of the current Common Travel Area in place between the UK and Irish Republic in the event of Brexit, suggesting that unless it was fully policed it could become a back-door route for "illegal immigration" from elsewhere in the EU.
But Ms Villiers rejected this, saying the agreement had been in place since 1923, was enshrined in UK law and would stay in place.
"The idea that thousands of non-Irish EU citizens would suddenly start crossing the border is far-fetched," she said.
"If we vote Leave and change the rules on free movement for non-Irish EU citizens, then if they come to the UK across our land border without legal clearance to do so, they would not be able to work, or claim benefits, or rent a home, or open a bank account and could ultimately be deported.
"There are plenty of mechanisms we can use to control immigration and deal with risks around illegal migration which do not involve physical checks at our land border."
Northern Ireland's political parties are split over the issue of EU membership, with the DUP backing the Leave campaign while Sinn Fein and others back Remain.