Tánaiste Simon Coveney and Northern Ireland Secretary Julian Smith are in Belfast for meetings with the five main Stormont parties as efforts to restore devolved government resume.
The latest process, which was initiated in the wake of the general election, was paused over the festive period after a pre-Christmas deal failed to materialise.
Three years on from the collapse of the devolved government, the Stormont parties have until a 13 January deadline to strike a deal to revive the institutions.
On that date, legislation to give civil servants additional powers to run Northern Ireland's struggling public services expires and Mr Smith will assume a legal obligation to call a snap Assembly election.
Mr Coveney urged the parties to show leadership and generosity.
He said the new year offered a chance for a new beginning and urged all sides not to disappoint the public again.
The leaders of the DUP and Sinn Féin used their respective new year messages to restate a desire to return to government.
DUP leader Arlene Foster said her party stood ready to restore devolution through a "fair and balanced deal".
"A Northern Ireland that is going to keeping moving forward must be one where everyone feels at home but must also be one where no one feels their culture is being marginalised," she said.
While Ms Foster warned that a focus on a potential border poll would lead to a "wasted decade", Sinn Féin president Mary Lou McDonald insisted a united Ireland was within reach.
Ms McDonald added: "There is no contradiction in working for Irish unity and working for the restoration of the Executive and Assembly - they are all part of the Good Friday Agreement.
"The outstanding issues can be resolved. The time for acrimony and division is over. The time for slogans and soundbites is over. The test now for every party that has talked up getting back to work is to go back to the Executive table and deliver."
Speaking this afternoon, DUP MP Jeffrey Donaldson said the petition of concern was just one of the issues where agreement remained to be reached.
"We want this done as quickly as possible but we also want to ensure that the agreement is fair and balanced, that it is sustainable, that the political institutions that are restored are sustainable, that we have a lengthy period of political sustainability," he said.
"We are not in the business of snatching at something because there is a deadline, we want Stormont restored and we want it restored as soon as possible."
Stormont imploded three years ago this month when the late Sinn Féin deputy first minister Martin McGuinness resigned in protest at the DUP's handling of a botched green energy scheme.
That dispute soon widened to encompass traditional rifts over issues such the Irish language and the toxic legacy of the Troubles.
A logjam over proposals to reform the petition of concern voting mechanism was one of the main reasons a deal failed to materialise before Christmas.
It was designed to protect minority rights but politicians have accused each other of misusing it for their own ends.
Discussions around change are focused on making it more difficult for one party to use the petition to block controversial legislation.
The latest push to restore powersharing broke up the week before Christmas, with UK and Irish governments singling out the DUP as the party standing in the way of a deal.
The party rejected the claims, insisting it would not be "bounced" into a "quick fix" that falls apart when tested.
Devolution can only be restored once the DUP and Sinn Féin - the region's two largest parties - agree terms to re-enter a mandatory coalition executive in Belfast.
The other three main parties - the SDLP, Ulster Unionists and Alliance - are also involved in the talks process convened by the UK and Irish governments.
While they could take positions in any new executive, their sign-off on a deal is not essential and a government could be formed in their absence, with those parties having the option of going into opposition.
Expectations of a breakthrough rose after the DUP and Sinn Féin both suffered bruising results in the general election.
With many interpreting the outcome as a public judgment on the parties' failure to do a deal, stalled efforts to restore the institutions appeared to gain fresh momentum in December.
However, proposals to reform a contentious cross-community voting mechanism in the Assembly have emerged as a key sticking point in efforts to finalise an agreement, with the DUP unhappy about what is being countenanced.
The DUP is also seeking changes to ensure the devolved institutions are more stable in future and cannot be readily pulled down.
Proposed legislative protections for Irish language speakers are another crucial element of the negotiations.
The Stormont parties are also seeking firm commitments from the UK government on a financial package to accompany the return of devolution - money that would likely be targeted at the region's crisis-hit health service.
Additional reporting: Tommie Gorman