DUP MP David Simpson has said it was premature for his party to decide to share power with Sinn Fein.
Mr Simpson and his Upper Bann assembly colleague Stephen Moutray issued a statement following Monday's meeting between Ian Paisley and Gerry Adams.
The pair expressed reservations about power-sharing in May, ahead of any "credible testing period".
But DUP South Down MLA Jim Wells said he was sticking with the party despite having his own reservations.
He said he had taken extensive soundings within his constituency and realised people wanted him to stay in the party.
Mr Wells, who was a deputy speaker in the last assembly, said outstanding issues could still "hamper" the party if not pinned down by 8 May.
"It is extraordinarily difficult, it is a situation where we were forced into the corner," he said.
"The Northern Ireland Office didn't organise a shotgun wedding, they brought the full firing team."
Mr Simpson said in his statement, first published in the Lurgan Mail: "It is for government, republicans and the leadership of our own party to now deliver what they have each promised.
"There must be no slippage or backsliding from any of them."
MEP Jim Allister is the only high-profile figure so far to resign from the DUP since Mr Paisley's meeting with the Sinn Fein leader.