Both the Irish and British governments have pledged to restore Stormont following the general election result.
In a telephone call on Friday evening, the taoiseach (Irish prime minister) congratulated Boris Johnson on his election victory.
They agreed the election had created a “significant opportunity” to restore the Good Friday Agreement institutions.
Both leaders said they would work closely with the Northern Ireland parties to help bring back devolution.
Stormont has been inactive since January 2017, when the DUP and Sinn Féin split in a bitter row.
The Prime Ministe, Boris Johnson, and Taoiseach Leo Varadkar agreed on the importance of a close relationship between the UK and Ireland.
Both also said that they looked forward to the smooth passage of the EU Withdrawal Agreement.
The Northern Ireland parties are set to meet on 16 December to try to end the Stormont stalemate.
The prime minister made clear in the phone call, his top priority is the restoration of a functioning Executive as soon as possible.
He said Northern Ireland Secretary Julian Smith will dedicate himself to the talks process.
The leaders both said they looked forward to meeting, in person, soon.
Mr Johnson updated the taoiseach on the timings for the reintroduction of the Withdrawal Agreement Bill next week and its passage through Parliament to ensure the UK leaves the EU on 31 January.