Sinn Féin and the SDLP have rejected the possibility of Stormont having a say over what kind of backstop may emerge if there is a ‘no deal’ Brexit
Proposals being worked on by the British government are said to include some kind of role for MLAs.
Sinn Féin and the SDLP said they oppose this.
Earlier the parties, along with Alliance and the Greens, were briefed on the Brexit talks by the EU’s chief negotiator, Michel Barnier.
The four parties have previously released joint statements expressing concerns about the impact of Brexit on NI.
The UK and the EU are still divided over how to solve the issue of the Irish border, less than two weeks before an EU summit on 17 October.
Sinn Féin vice-president Michelle O’Neill said a role for MLAs would be unacceptable, while SDLP leader Colum Eastwood said it would give the DUP a veto but that it would not happen.
Ms O’Neill said the Mr Barnier told her during the meeting that the Brexit summit later this month in Brussels would be decisive
The delegation also met the EU Brexit co-ordinator Guy Verhofstadt.
Speaking ahead of the meeting, Sinn Féin vice-president Michelle O’Neill told the BBC: “I think the EU has heavily invested in our peace process both politically and financially down through the past 20 years, so they need to remain firm on their commitment.
“I welcome the comments they have made, but as we reach this crucial stage, it’s vital that we go out collectively and make the case once more to Michel Barnier.”
The Alliance deputy leader, Stephen Farry, said it was important to “de-dramatise” the issue.
“We need to see an end of talk of political and constitutional crises and for people to recognise the backstop for what it is – a pragmatic intervention designed to address the needs of Northern Ireland,” he said.
Green MLA Steven Agnew said “the UK and EU must stay in some form of a customs union and single market to protect our economic and social prosperity”.
SDLP leader Colum Eastwood added: “We do not need a new border in Ireland and we do not need a new economic border in the Irish Sea.
“We are confident that Monsieur Barnier will continue to push for a deal with Britain that protects people in Ireland.”
It is understood UK officials are working on proposals to break the impasse over the border backstop issue.
It would include a “hybrid backstop” and “light touch” regulatory checks on goods going between Great Britain and the EU.
There is also the possibility of some kind of democratic oversight by Stormont and a proposal to include all of the UK in the customs union for a time-limited period.
The DUP has already expressed opposition to a hybrid backstop – Nigel Dodds MP told the BBC his party could not accept a “separate hybrid model” in which Northern Ireland is in the EU single market but out of its customs union.
It remains to be seen if the EU will accept the plan.
Politicians from the DUP and UUP are due to travel to Brussels next week.