Tánaiste Simon Coveney and Northern Ireland Secretary Julian Smith have met the five main parties at Stormont.
A number of participants described the round table meeting as positive.
But it is unlikely that an agreement to restore power-sharing will be in place before Christmas.
The parties began the latest attempt to broker an agreement on Monday. They have a deadline of 13 January to do so.
The administration collapsed almost three years ago amid a row about a botched green energy scheme.
The rift soon widened and refocused on long-standing disputes over issues such as the Irish language and same-sex marriage.
With same-sex marriage having been legislated for at Westminster earlier this year, the wrangle over the Irish language remains the key stumbling block.
If a devolved executive is not resurrected by 13 January, legislation that gives the civil service extra powers to run public services will expire.
Mr Smith will then be likely to call a snap Assembly election.
After the initial meetings on Monday, Mr Smith described the mood as "positive" and said he detected a willingness to strike a deal.
Mr Coveney said they would work "night and day before Christmas, and again in the New Year" to get a deal.
Additional reporting PA