SDLP leader Colum Eastwood said his party will not nominate another infrastructure minister to sit in a “zombie executive”.
He led his reduced team of MLAs to Stormont on Monday following a bruising election which saw the SDLP MLA total drop by four to eight.
Their losses included their deputy leader and outgoing infrastructure minister Nichola Mallon in North Belfast and veteran Dolores Kelly in Upper Bann.
Ministers remain in post until a new executive is nominated.
Mr Eastwood said it would be undemocratic for his party, which he said no longer had a mandate for the executive, to be in the executive.
He urged DUP leader Sir Jeffrey Donaldson to nominate ministers for a new executive.
“From our perspective, we’re now in opposition, we will act constructively, work with other parties but we will also hold ministers to account where we have to,” he said.
“We don’t have a mandate for government, the people have spoken.
“I respect what the people have said, they’ve made it very very clear.
“We don’t have enough seats in the Assembly to form a government.
“I don’t feel good about that but I’m humbled about it.
“We can’t be in government, it would be totally undemocratic for us to sit in a zombie executive and have no power to do anything when we haven’t even got a mandate from the people.
“We know who got the mandates, we will support them when we have to, we will also hold them to account, but they should get on with it today and form a government.”
Mr Eastwood said a government needs to be formed urgently.
He said: “I call on Jeffrey Donaldson to commit to appointing a deputy first minister right away, people can’t wait any longer.
“We’ve a cost-of-living crisis, we have a waiting-list crisis which is out of control and that government needs to be formed today,” he said.
“Michelle O’Neill has been elected as first minister of Northern Ireland.
“That has to be respected, has to be acted upon and an Executive has to be formed.”