Video report by ITV News Political Correspondent Paul Brand
Journalist Lyra McKee's death "must not be in vain", according to Northern Ireland Secretary Karen Bradley, who urged both sides to find a solution to the Stormont deadlock.
Speaking at a press conference today, Ms Bradley announced talks would resume on May 7 to try and break the impasse which has blighted Northern Ireland's devolved government for more than two years.
The announcement on Friday comes just two days after the funeral of murdered journalist Ms McKee, 29, who is believed to have been murdered by the New IRA.
Ms Bradley said the "sickening" murder of Ms McKee had "deeply shocked everyone across the world".
ITV News Political Correspondent Libby Wiener says the beginning of talks is a "hugely significant moment", but adds "major differences" between both sides remain
She added: "Since Lyra's death, communities across Northern Ireland and the political spectrum have come together, united in condemnation at this murderous act.
"They have delivered a clear message - the people responsible for this act of terrorism have absolutely nothing to offer Northern Ireland and have no place in society."
Ms Bradley said: "There remain small numbers of dissident republicans who remain intent on killing.
"Our challenge is to ensure that we continue to work for peace for the whole community."
Ms Bradley added: "Lyra symbolised the new Northern Ireland and her tragic death cannot be in vain.
"All of us must take inspiration from what Lyra achieved in her life and work even harder to make Northern Ireland a brighter, more peaceful and prosperous place for everyone."
It appears political leaders from all sides have been moved into action following the funeral of Ms McKee.
During the service, Catholic priest Father Martin Magill received a standing ovation from those in attendance when he questioned why it had taken the death of a journalist to get the political leaders in a room together.
Ms Bradley appeared alongside Irish Minister for Foreign Affairs and Trade Simon Coveney, who said: "This can be done. When you think about the agreement that was made 21 years ago and the obstacles they needed to overcome then, the challenges we face today pale into the background in comparison.
"Yes, we have difficult choices to make. The polarisation of politics in Northern Ireland, particularly in the last 12 months, poses real challenges. "There are trust issues - let's not pretend there isn't - and we will have to try to overcome them.
"But having spoken to all the parties in the last few days, I believe there is an appetite to try and I can tell you the two governments are determined to assist that process in a way that will get it across the line."
Theresa May and Leo Vardakar called for "new thinking" to help break the deadlock, which emerged out of a snap election in 2017 which brought an end to Stormont's unionist majority and saw DUP's lead over Sinn Fein cut from 10 seats to one.
Mrs May and Mr Varadkar said: “We also heard the unmistakable message to all political leaders that people across Northern Ireland want to see a new momentum for political progress.
“We agree that what is now needed is actions and not just words from all of us who are in positions of leadership.”
Sinn Fein has rejected DUP leader Arlene Foster's offer to move the political impasse in Northern Ireland.
The British and Irish premiers said: “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 Northern Ireland Executive, Assembly and North-South Ministerial Council – so that they can effectively serve all of the people for the future.”
The Prime Minister and Taoiseach added: “We understand the complexity of the underlying concerns of all parties, and the need for renewed trust, mutual respect, generosity and new thinking to resolve the issues.
“As Prime Minister and Taoiseach, we are determined to work together to ensure this process comes to a successful conclusion.”
Progress on the talks will be reviewed at the end of May and an agreement has been reached on a British-Irish Intergovernmental Conference in the same period.
Each side has blamed the other for the break-down in talks previously.
Mrs Foster wants a twin-track approach where devolved institutions are restored to deal with issues like running the health service, while a separate process addresses disagreements over same-sex marriage.
Sinn Fein deputy leader Michelle O'Neill rejected that approach, saying issues like marriage equality and protection for Irish language must be delivered.