The new Northern Ireland Secretary, Karen Bradley, has met the Irish Foreign Affairs Minister Simon Coveney.
Following the meeting in London, Mrs Bradley said they both wanted the restoration of devolved government as soon as possible.
She said she would reflect on the conversations she had with Mr Coveney and Northern Ireland's political parties over the weekend.
Mr Coveney said he was looking forward to working with Mrs Bradley.
"I think we know there are significant challenges ahead but also I think there is a desire across all parties in Northern Ireland and indeed both governments to find a way to help to facilitate the re-establishment of a functioning executive that involves all the parties," he said.
Prior to the meeting, it was described by one official as a "getting to know you" session - an opportunity to establish personal relationships.
It was the first time the pair have met since Karen Bradley was appointed Northern Ireland Secretary earlier in the week.
It has been a baptism of fire for Mrs Bradley.
On Monday, she was moved from her job as culture minister and made secretary of state after James Brokenshire stood down for health reasons.
She came to Belfast on Wednesday and met the main Northern Ireland parties.
In the days ahead, there will be an expectation that Mrs Bradley needs to map out how a new talks process could work.
Northern Ireland has been without a devolved government since 9 January 2017, when Sinn Féin pulled the plug on its power-sharing coalition with the Democratic Unionist Party (DUP).
They have failed to find a resolution in spite of several rounds of talks.