Mrs Foster said her staunchly unionist party had been contacted by nationalists and republicans in the wake of Ireland’s landslide referendum decriminalising terminations.
Speaking to Sky News she said they recognised the DUP was “the only party that supports the unborn”, after calls political spectrum for Northern Ireland strict laws to be eased in the wake of the Irish vote.
Abortion is illegal in all but the most exceptional of circumstances in Northern Ireland and Mrs Foster has already insisted any change should be a matter for the assembly in Belfast - which has been suspended for months.
Sinn Fein currently supports it in extreme cases, like foetal abnormality. However, the republican party is due to consider whether to change to support unrestricted abortion up to 12 weeks at its ard fheis (party conference) later this month.
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In an interview to be broadcast on Ridge on Sunday, Mrs Foster told Sky there were people across Northern Ireland who “who feel so very strongly about this issue that they will cast their vote on that basis”.
She said: “I have had emails from people in the Republic of Ireland feeling very disenfranchised about what has happened in the Republic of Ireland.
“I have had emails from Nationalists and Republicans in Northern Ireland not quite believing what is going on and saying they will be voting for the DUP because they believe we are the only party that supports the unborn.”
Some 66.4% of Irish voters in May’s referendum backed repeal of the controversial Eighth Amendment of the constitution, which bans abortion in all but exceptional circumstances.
Mrs Foster criticised some of the celebrations by those who supported the repeal, telling Sky: “It certainly does not deserve some of the antics that we’ve seen recently frankly and I did find it, I have to say, quite distasteful to see people dancing about on the streets in relation to the referendum results.
“This is a serious subject.”
UK Prime Minister Theresa May faces a political headache over calls to act because her fragile administration depends on the support of the 10 DUP MPs.
Westminster politicians in favour of a change have suggested the forthcoming Domestic Abuse Bill promised by ministers could be used as a vehicle for MPs hoping to change the law in Northern Ireland.
The devolved Stormont Assembly has not sat for months following a row between former coalition partners the Democratic Unionists and Sinn Fein over a botched green energy scheme.