Mr Poots nominated Mr Givan to stop the collapse of the Stormont Assembly: Sinn Féin refused to re-nominate Michelle O'Neill as Deputy First Minister unless they could have a guarantee that the Irish language act, which would give official status to both Irish and Ulster-Scots, would be legislated before the summer break.
Mr Poots was described as failing his first real test of his leadership after being in the job for just 21 days.
Arlene Foster, former leader of the DUP, formally stood down as First Minister on 14 June.More news: UK, Australia agree post-Brexit trade deal
Senior DUP figures have gathered for a meeting at party headquarters in Belfast, amid anger in the party that Northern Secretary Brandon Lewis announced early on Thursday morning that a compromise had been reached over the introduction of Irish language legislation, as reported by the Irish Times.
Ireland's largest nationalist party, the Sinn Féin party, insisted on a nomination involving the implementation of the cultural elements of a political agreement mediated by London and Dublin, and reinstated the administration three years later without delegation.
The members were unhappy that Mr Poots had agreed to enter a coalition on that basis.
He said he had been asked by the party to remain in post until his successor is elected.More news: Vietnam to receive a million Covid vaccine doses by July
"This has been a hard period for the party and the country and I have conveyed to the chairman my determination to do everything I can to ensure both unionism and Northern Ireland is able to move forward to a stronger place".
DUP group leader on Derry City & Strabane District Council, Hilary McClintock, explained that people will have to put their name forward and the party will make a decision on it.
A meeting of DUP party officers got under way on Thursday, with the recently appointed leader facing a major revolt.
Mr Poots, who took over as leader from Ms Foster in May, narrowly defeated Sir Jeffrey in a leadership vote by only two votes.More news: Justice Department under Trump seized data from House Democrats in leaks inquiry