Taoiseach Leo Varadkar has spoken by phone with British Prime Minister Boris Johnson this evening.
A spokesperson for Mr Varadkar said he had congratulated the prime minister on his election victory.
They agreed there was now a significant opportunity to restore the Good Friday Agreement institutions and they pledged to work with the Northern Ireland parties to achieve this.
They also discussed how to strengthen the bilateral relationship between Ireland and the UK.
Both looked forward to the smooth passage of the Withdrawal Agreement.
They agreed to stay in close contact in the period ahead.
A Downing Street spokesperson said: "In relation to Northern Ireland, the Prime Minister made clear that his top priority is the restoration of a functioning Executive as soon as possible.
"He said that the Secretary of State for Northern Ireland, Julian Smith, will dedicate himself to a talks process ensure the devolved institutions are restored."
Earlier, Mr Varadkar said Britain's exit from the European Union would now go ahead and that it will be an exit "with the Withdrawal Agreement which we negotiated".
He added a transition period would run throughout 2020 during which "nothing will change".
Speaking on RTÉ's Six One, Mr Varadkar said: "No matter what happens, we know there won't be a hard border between north and south."
However, he said what had yet to be resolved was the "long term trading relationship" between the EU and the UK which was important.
Mr Varadkar earlier said the political tectonic plates were shifting in Northern Ireland following last night's election results.
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Speaking in Brussels, he said: "There were very significant results in Northern Ireland. If you know about plate tectonics you know that things move slowly, then things move suddenly.
"Slowly because of demographics and more suddenly because of the reaction of people in Northern Ireland to Brexit."
The Taoiseach said there was no longer a unionist or nationalist majority in the North, adding that the centre ground was expanding, a trend he said had been confirmed in elections to the Assembly and European Parliament.
Asked by the BBC if a united Ireland was more likely now, he said: "People shouldn't race ahead of themselves with other plans.
"What hasn't changed is that the future for us in Ireland is reconciliation, it's power-sharing, it's closer cooperation between north and south and also between Britain and Ireland, and that's the philosophy underpinning the Good Friday Agreement."
Mr Varadkar said all sides should strive to restore the Assembly and Executive by the deadline of 13 January.
He said: "We'll be giving this everything between now and January to get the Assembly and Executive up and running.
"If at that point there is no power-sharing restored in Northern Ireland, we're then looking into another assembly election in Northern Ireland, and I can't imagine who would really want that."
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Mr Varadkar congratulated Mr Johnson on what he called "an enormous victory on a personal level" and a "very clear result" for the Conservative Party and said the decisive outcome was a positive thing.
"We had for a few years, a parliament that wasn't able to form a majority around anything.
"We now clearly have a majority in the House of Commons to ratify the withdrawal agreement, so the next step is to ratify the Withdrawal Agreement", he said.
Mr Varadkar said he was "keen to work very hard" with Mr Johnson to "get the executive in Northern Ireland up and running".
He said this was "absolutely crucial" and has to be a "key priority".
Asked about the next stage of the Brexit process, the Taoiseach said: "What I'd like to see is a new future economic partnership, a trade deal plus, between the UK and the EU, including Ireland."
However, he warned that the EU will insist on the UK not undercutting Europe with a low regulation economy post-Brexit.
Mr Varadkar said: "I'd like to ensure we still have tariff-free and quota-free trade between Britain and the EU and that there's a set of minimum standards so that nobody feels there's unfair competition, that anyone is trying to undercut them when it comes to labour rights, environmental protections and issues like that."
Congratulations to @BorisJohnson on his victory in the UK General Election. The Irish government and my department now stand ready to seize the moment and focus on getting #Stormont up and running for all the people and parties in Northern Ireland.— Simon Coveney (@simoncoveney) December 13, 2019
Tánaiste and Minister for Foreign Affairs Simon Coveney also congratulated Mr Johnson and said the Government is "ready to seize the moment and focus on getting Stormont up and running again".
The Conservative Party won an overall majority in the House of Commons, a result that will enable Mr Johnson to pass the Brexit legislation required for the UK to leave the EU.
Minister of State for European Affairs Helen McEntee said the UK election result brings certainty around Brexit and the focus and energy of the Government will now move to the next phase of the trade negotiations.
Additional reporting Tony Connelly