Prime Minister Theresa May and Taoiseach (Irish PM) Leo Varadkar have issued a joint statement setting up a new talks process aimed at restoring Northern Ireland devolution.
Northern Ireland has been without a government since January 2017.
Earlier this week, the two premiers attended the funeral of journalist Lyra McKee.
At the funeral, priest Fr Martin Magill asked why it had taken her killing to unite politicians in Northern Ireland.
This was followed by a series of calls for a fresh round of talks, aimed at reviving the power-sharing government at Stormont.
“In coming together with other political leaders in St Anne’s Cathedral to pay tribute to Lyra McKee, we gave expression to the clear will and determination of all of the people of these islands to reject violence and to support peace and a better future for everyone in Northern Ireland,” they said.
Successful conclusion may prove tricky
By Gareth Gordon, BBC News NI Political Correspondent
Northern Ireland Secretary Karen Bradley had already said she planned to hold talks about Stormont after the local government elections next Thursday.
But several parties wrote urging her to convene discussions urgently in the wake of the killing of journalist Lyra McKee.
It is understood there were intensive discussions in Belfast after Wednesday’s funeral which was attended by leading politicians from Northern Ireland, the Republic and Westminster.
But convening talks is one thing.
Concluding them successfully with many outstanding issues between the DUP and Sinn Féin, not to mention Brexit, is another.
“We have agreed to establish a new process of political talks, involving all the main political parties in Northern Ireland, together with the UK and Irish governments, in accordance with the three stranded process.
“The aim of these talks is quickly to re-establish to full operation the democratic institutions of the Belfast/Good Friday Agreement – the NI executive, assembly and North-South Ministerial Council – so that they can effectively serve all of the people for the future.”
The statement added: “We have asked the secretary of state for Northern Ireland and the tánaiste [Irish deputy prime minister] to meet later today in Belfast to set out our proposed approach and to commence the talks process as soon as possible after the local elections in Northern Ireland.”
The talks are expected to begin as soon as possible after next week’s local elections in Northern Ireland.
The two governments are to review progress at the end of May.
Both premiers have also agreed that that there should be a meeting of the British-Irish Intergovernmental Conference during the same period.
“The conference will consider East/West relations, security cooperation, and political stability in Northern Ireland,” they said.