Northern Ireland should not be "punished" by political rivals while Brexit laws are prepared, the SDLP said.
Leader Colum Eastwood urged the British and Irish Governments to reconvene a British-Irish Intergovernmental Conference to "clear the decks" and allow restoration of political powersharing.
Stormont has not sat for months in a row over a botched green energy scheme which led to the resignation of former deputy first minister Martin McGuinness, collapse of the institutions, and deadlock between former coalition partners Sinn Fein and the DUP.
Mr Eastwood said: "The SDLP will not allow our people to be punished by those who have trapped powersharing in stalemate - and both Governments should ensure that is the case.
"Those who claim to be true to the spirit of the Good Friday Agreement now must act. The consequences of doing nothing will be catastrophic."
Last week, the Withdrawal Bill passed through the legislatures of Westminster.
Mr Eastwood added: "This legislation is soon to be made law without the consent of the people of Northern Ireland."
Northern Ireland Secretary Karen Bradley took part in the British-Irish Council in Guernsey last week.
The first ministers of Scotland and Wales were also at the summit.
It was the 30th meeting of the body, which was set up under the 1998 Good Friday Agreement.
Mr Eastwood added: "It has been several months since the SDLP told both Governments to reconvene the British-Irish Intergovernmental Conference to clear the decks and let us get back to powersharing.
"Yet, we have seen no progress whatsoever. It isn't good enough.
"Today I have issued a memo to both the Secretary of State and an Tanaiste calling for progress. Asking that both Governments do not allow this dangerous drift to continue anymore.
"Northern Ireland is being left behind in too many ways. People here deserve better, they deserve Government and they deserve to have their rights, protected by the Good Friday Agreement, safeguarded by both guarantors."