Sinn Fein and the DUP have both pledged to approach talks to restore power-sharing positively and have acknowledged that people want to see devolution restored.
Negotiations are set to resume on Thursday at Stormont after they were paused over the Christmas holidays.
Secretary of State Julian Smith is flying in to Northern Ireland tomorrow to make himself available to party leaders before the formal dialogue begins.
He has said that if a deal isn't brokered by January 13 he will call a fresh Assembly election.
DUP MP Gregory Campbell said: "The recent Westminster election results can be interpreted as giving voice to the exasperated desire of many people to see a Stormont government up and running to try and deal with the extreme circumstances that abound in health, education and other sectors in our society.
"For our part, we will play our full role in securing ministerial-led government in Northern Ireland."
Sinn Fein president Mary Lou McDonald said: "The outstanding issues can be resolved.
"The time for acrimony and division is over, and 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.
"It is in the interests of all our people that we establish good government and real power-sharing based on equality and respect."
Alliance leader Naomi Long commented: "The deadline is approaching and we know the issues on the table. If people are serious about reaching a deal and showing leadership, it can be achieved quickly."
SDLP Leader Colum Eastwood said: "For almost three years we have been without a government to deal with hospital waiting lists, pay parity for healthcare workers, the funding crisis in our schools and the welfare cliff edge about to hit tens of thousands of families. It's time to get back to work.
"With less than two weeks to secure a resolution, all parties must be prepared to stretch themselves in the substantial common interests of all our communities."
UUP leader Steve Aiken added: "Northern Ireland needs accountable, responsible and sustainable devolved government. This can only be delivered through fundamental reform.
"If the talks fail to deliver those reforms, then there will be no point in restoring institutions which are built on sand.
"They will almost certainly fall back into the bad habits of the past, eventually leading to their inevitable collapse.
"It's either deliver sustainable devolved government or else move to direct rule. The health service, our schools and our people cannot afford any more false dawns."
TUV leader Jim Allister said no unionist should agree to "weaponised Irish language" legislation.
"However it is dressed up, those who concede such on their watch are actively complicit in the de-Briticising of this part of the UK," he said.
"Make no mistake, Irish language demands are not linguistic, but political. The Irish language is already generously feted, with its own education sector, its own North/South executive body and lavish funding. What is playing out is a political strategy of 'Brits Out' mentality to make unionists uncomfortable in their own land."