Update 8pm: The Taoiseach has told the British Prime Minister that the Irish Government does not want to see a return to direct rule in Northern Ireland.
Leo Varadkar spoke to Theresa May by phone this evening, following his meeting with Sinn Féin leaders Mary Lou McDonald and Michelle O'Neill in Dublin.
The Government also emphasised its "full commitment to the Good Friday Agreement" stating that it must be "must be implemented in full".
The statement comes after DUP leader Arlene Foster said earlier today that she has asked the Northern Secretary to set a budget for Northern Ireland.
"An Taoiseach, Leo Varadkar spoke with the British Prime Minister, Theresa May by phone this evening," a Government statement read.
"This followed a meeting between the Taoiseach and Tánaiste Simon Coveney with Mary Lou McDonald TD and Michelle O'Neill MLA this evening to review recent developments in Northern Ireland.
"The Taoiseach emphasised the Government's full commitment to the Good Friday Agreement, and its determination to secure the effective operation of all its institutions.
"As co-guarantor to the agreement, the Government will continue to engage with the parties in Northern Ireland and the British Government to support the urgent formation of a new Executive by the mandated political parties.
"The Government's firm position is that the Good Friday Agreement and subsequent agreements must be implemented in full, and in this context the Taoiseach and Tánaiste re-iterated that the Irish Government does not want to see the introduction of direct rule in Northern Ireland."
Earlier: No deal until Irish language issue is dealt with, says Mary Lou McDonald
Update 5.52pm: Sinn Féin President Mary Lou McDonald has today rubbished claims blaming her party for the collapse of powersharing talks in Northern Ireland.
She is meeting with the Taoiseach and Tánaiste this evening to discuss whether there can be a quick re-start of negotiations to form a government in the North.
Earlier, DUP leader Arlene Foster has asked the British government to step in to set a budget and make policy decisions for Northern Ireland.
Ms McDonald opposes the idea of direct rule from London, but said that key issues remain unresolved.
"Be in no doubt - there will be no resumption of the institutions until the matter of An Gaeilge is dealt with," she said.
"Be in no doubt also that there is a solution to this, and the solution was arrived at by the parties and we are, as I said earlier, very, very disappointed that the DUP chose not to bring that over the line."
Earlier: Arlene Foster asks British government to press ahead with setting budget for Northern Ireland
Update 5.07pm: DUP leader Arlene Foster has said that she has asked the Northern Secretary to set a budget and make key decisions on schools, infrastructure and hospitals in Northern Ireland.
Ms Foster said that she will be raising this issue again in the British Parliament tomorrow.
She added that she stands ready to form a devolved government tomorrow without any pre-conditions.
Earlier today, an official spokesman for British Prime Minister Theresa May said that the British government is working towards getting the devolved administration at Stormont up and running again, and is "fully committed" to the Good Friday Agreement.
Former Northern Ireland Secretary Owen Paterson recently retweeted a commentator's suggestion that the 1998 accord which largely ended decades of violence had outlived its use.
Northern Ireland Secretary Karen Bradley is due to update Parliament on the Stormont impasse tomorrow.
Mc May's official spokesman said: "The government remains fully committed to the Good Friday Agreement and we continue to work towards getting the devolved administration up and running again.
"It is disappointing that agreement has not yet been reached between the parties, but we do still believe that the basis for an accommodation exists."
The Easter agreement was signed almost 20 years ago between the British and Irish Governments and enjoyed support from most of the major parties in Northern Ireland. Ian Paisley's DUP opposed it.
It enabled the formation of a ministerial Executive and Assembly at Stormont.
The Irish Government has repeatedly stressed the need to protect the Agreement.
Mr Paterson was Northern Ireland Secretary from 2010.
He also tweeted that Northern Ireland deserved good government, and health services were falling behind the rest of the UK without a devolved Executive.
Earlier: SF helped drum up support for letter urging Taoiseach to seek law changes in the North
Sinn Féin mobilised its base in the Republic of Ireland to garner support for a letter from high-profile members of civic society urging the Taoiseach to push for law changes in Northern Ireland.
The letter from 100 prominent people in fields such as sport, law and the arts calls on Leo Varadkar to ensure citizens north of the border have the same rights as those in his jurisdiction.
A similar public letter was sent to the Taoiseach signed by high-profile nationalists in the North before Christmas.
The latest letter - signed by well-known names such as musicians Christy Moore, Damien Dempsey, Glen Hansard and Frances Black - presses Mr Varadkar to lobby for legislation for Irish language speakers and same-sex marriage in Northern Ireland - two of the key sticking points in the Stormont powersharing talks.
It also urges the Taoiseach to take action to ensure families impacted by the Troubles can get timely access to the courts. Long-running delays to conflict-related inquests is another unresolved issue at Stormont.
An email obtained by the Press Association indicates that Sinn Féin was involved in an organised nationwide effort to find individuals willing to sign the letter.
The email sent last week by a senior party officer in the Republic of Ireland to council leaders across the country read: "We are seeking support from public figures at local and national level in the areas of the arts, culture, legal, business, community etc and so far have some 70 signatories including Christy Moore, Damien Dempsey, Glen Hansard and Frances Black.
"But there are also many more signatories without a national profile but who are well known in communities for the work that they do. And this is where you come in...
"We are looking for your help to get this up to 100 by the end of the day.
"Please get in touch with suggested names as well as a link person who will contact them."
A Sinn Féin spokesman confirmed the party assisted in the endeavour.
"We were asked to assist by the organisers of this initiative in garnering support for a civic lobby in support of the rights-based agenda in the North," he said.
"We are happy to do so, to give voice to the frustrations felt throughout Irish civic society at the denial of basic rights in the North."
The December letter was signed by well-known names such as All-Ireland-winning Tyrone GAA captain Peter Canavan, Republic of Ireland and West Brom footballer James McClean and Olympic boxers Paddy Barnes and Michael Conlon.