Sir Jeffrey Donaldson has dampened optimism expressed by Ireland's Foreign Affairs Minister Simon Coveney, who said on Thursday that the Executive could hopefully be restored within weeks.
Sir Jeffrey said on Friday that while progress was being made in the talks aimed at restoring the powersharing institutions, a "question mark" still remains over whether a deal could be struck between the DUP and Sinn Fein.
When asked if he shared Mr Coveney's optimism, the Lagan Valley MP said: "We have been making progress in the talks and there has been a more meaningful engagement in the last couple of weeks between the parties, but there remain gaps between us."
He added: "We will continue to work at it. We absolutely want to see an Executive up and running as soon as possible.
"But it is difficult to predict at this stage when we might get agreement and if we will get agreement - there remains a question mark.
"Progress is being made but that does not mean in the end there will be an agreement, but we are determined to do our best to get one."
Sinn Fein and the DUP have been at loggerheads since the collapse of the Assembly in January amid a bitter row between the two main parties about a botched green energy scheme.
Several rounds of talks have so far failed to reach an agreement.
For several months, one of Sinn Fein's main demands before returning to the Executive was that DUP leader Arlene Foster step aside as First Minister until the conclusion of a public inquiry into the Renewable Heat Incentive (RHI) scandal.
When asked if this was still a red line for the republican party in the talks process, Sir Jeffrey said: "I don't want to comment on the specifics of the negotiations, but we are pleased with progress that has been made, but there are still issues to be resolved."
Sir Jeffrey's comments are at odds with Mr Coveney's optimism on Thursday.
Following meetings with the DUP and Sinn Fein in Belfast, Mr Coveney said the "mood between the two parties has improved a lot" and that a "relatively small" number of issues remained to be resolved.
He added that "hopefully a fully inclusive executive (would) be in place within the next number of weeks".
Both Mr Coveney and Taioseach Leo Varadkar have warned that the current instability in the region "is not a sustainable situation for much longer", particularly with serious issues like Brexit and the Bombardier crisis to be dealt with.