Sinn Féin, the SDLP and the Alliance Party have criticised the DUP for failing to take part in a meeting of ministers from Belfast and Dublin.
The DUP is boycotting some North-South Ministerial Council (NSMC) meetings due to their opposition to post-Brexit arrangements for Northern Ireland.
On Friday, a meeting involving the Irish Transport Minister Eamon Ryan did not take place.
First Minister Arlene Foster said no-one from her party was able to attend.
The NSMC is the main body for cross-border co-operation between the governments of Northern Ireland and the Republic of Ireland.
Stormont Infrastructure Minister Nichola Mallon claimed the meeting had been "blocked from proceeding because no accompanying unionist minister would make themselves available".
"The DUP's obstruction is a deliberate act to undermine the Good Friday Agreement," said the SDLP deputy leader.
"Their tactic of disruption and delay isn't going to work."
Alliance Party leader and Justice Minister Naomi Long tweeted that it was "the second NSMC meeting in as many weeks to be obstructed in this way" and described it as "simply unacceptable".
She said it was "another reason why the binary structures need reform".
"Ministers shouldn't need 'minders' from 'the other sort' to proceed with business," she said.
Communities Minister Deirdre Hargey of Sinn Féin also criticised the DUP position and said unionist ministers "do not get to cherry-pick which meetings or structures they want to participate in".
"It's an obligation and must be fulfilled," she said.
"Properly functioning north-south structures are critical to the successful operation of the Good Friday Agreement framework."
Speaking on Friday, Mrs Foster, the DUP leader, said it was not possible to attend Friday's meeting as there "wasn't anyone available".
She said the party was "looking at alternative dates and we'll get a date in the near future".
Mrs Foster denied it was DUP policy to boycott NSMC meetings.
"All of these meetings take place in agreement - the agenda wasn't agreed, nothing was agreed between the parties but it's something that will happen in the future," she said.