Irish Foreign Affairs Minister Charlie Flanagan has said he is optimistic a Belfast power-sharing deal can be done within the three-week legal deadline.
But Mr Flanagan has played down the significance for politics in the Republic of Sinn Fein gains in the Stormont election.
He again utterly ruled out any prospect of a Fine Gael-Sinn Fein coalition, saying its economic policies were "completely different".
Mr Flanagan, who is due in Belfast later this week, said he was heartened by contacts with all the main parties yesterday.
He spoke yesterday morning with Secretary of State James Brokenshire, and with several of the main party leaders in Northern Ireland.
He believed there was a deal of goodwill to get down to government-making talks as soon as possible.
But he would not comment on the impasse over Sinn Fein demands that DUP leader Arlene Foster, (right) stand aside pending investigation of the 'cash for ash' controversy. He said he would talk with Mrs Foster himself in the coming days.
The Foreign Affairs Minister ruled out any extension of the legal three-week time limit for Executive formation. He also utterly ruled out a move to direct rule by London.
"Given that Brexit talks are about to begin later this month we need this government in all haste. There was a huge turnout in last Thursday's election and the primary message from voters was that they demanded effective government to deal with Brexit," Mr Flanagan said.
Mr Flanagan added the outcome of the vote, with Sinn Fein less than 1,200 votes short of finishing ahead of the DUP, had no real implications in the Republic.
He said the circumstances of the election, and the high voter turnout, was mainly motivated by factors in Northern Ireland.
Mr Flanagan said after speaking to Mr Brokenshire that "it was of the utmost importance for the people of Northern Ireland that the political institutions, established under the Good Friday Agreement, promptly resume their work, not least so that they can effectively engage with the issues raised by Brexit".
He said there is a need for immediate discussions with the parties in Northern Ireland focused on two main areas: addressing outstanding issues, including the implementation of past agreements and addressing the legacy of the past; and on the formation of a new power-sharing Executive. Both parts of these discussions are essential and inter-dependent," he said.
"Dealing with outstanding issues from previous agreements will be necessary to create confidence at this critical moment for devolution in Northern Ireland.
"All parties eligible to nominate Ministers to the Executive will be invited to participate in these discussions which, in accordance with previous agreements, will be facilitated by the two Governments.
"Particular responsibilities attach to the two parties who are entitled to nominate a First Minister and Deputy First Minister to engage with each other, and to advance discussions with all eligible political parties, on the formation of a new Executive."
Mr Flanagan said "the heart of the Good Friday Agreement is its interlocking political institutions. They can only be sustained on the basis of partnership, equality and mutual respect".
"As a co-guarantor, the Irish Government is determined to uphold the principles of the Agreement and to protect its institutions. In the coming weeks, we will work with all concerned to see the power-sharing Assembly and Executive restored to effective and harmonious operation," he said.
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