DUP MP Sammy Wilson has accused the Irish government of trying to "tear up" the Good Friday Agreement.
His comments came after Taoiseach (Irish PM) Leo Varadkar said a no-deal Brexit could lead to a united Ireland.
Mr Wilson said he was seeking a border between Britain and NI and accused the Irish government of casting aside the principle of consent for the border.
However, Sinn Féin leader Mary Lou McDonald said Mr Varadkar should form an "all-Ireland forum on Irish unity".
On Friday, Mr Varadkar said the possibility of a no-deal Brexit was a "British threat" and that he hoped it was an option new Prime Minister Boris Johnson would not choose.
Mr Johnson has said a Brexit deal would require the EU to "abolish" the controversial Irish border backstop, but the EU has said the backstop would not be removed from the current withdrawal agreement, negotiated by Mr Johnson's predecessor Theresa May.
What is the backstop?
The backstop is a key piece of the deal negotiated by his predecessor's government, dictating what will happen to the border between Northern Ireland and the Republic of Ireland.
It is a last resort that guarantees a frictionless border if no better solution is devised in time - by maintaining close ties between the UK and the EU until such a solution is found.
Mr Varadkar said a "no deal" could end with "liberal Protestants, liberal unionists starting to ask the question as to where they feel more at home".
But Mr Wilson told Irish broadcaster RTÉ that while "there are many unionist who voted to stay within the European Union that didn't mean they wanted to leave the union of the United Kingdom".
He said "the kind of shenanigans we're seeing from government in the Irish Republic" would make people more determined to avoid a united Ireland.
"It is the Irish Government who are pushing for the Belfast Agreement to be torn up, the principle of consent to be cast aside and for a border to be placed between Northern Ireland and Britain, the country to which we belong, the country to which is our biggest source of income and source of trade," he added.
Meanwhile, Mary Lou McDonald, Sinn Féin's president, said Mr Varadkar "should make clear in the event of a no-deal Brexit, that Irish unity is the solution to averting a hard border on our island".
"There is nothing provocative about wanting a united Ireland and the government has a responsibility to lead from the front," she added.
"There is a momentum building for Irish unity and we need political, institutional and legislative arrangements in place to manage that.
"That preparation must include the convening of an all-Ireland forum on Irish unity without delay."