They are meeting to continue discussions aimed at restoring the power-sharing Executive in Northern Ireland.
The 1998 Good Friday Agreement - also referred to as the Belfast Agreement - commits the United Kingdom and Irish Governments to demonstrate "rigorous impartiality" in their dealings with the different political traditions in Northern Ireland.
Mrs May ordered Ministers from different government departments to meet and ensure everything possible was being done to assist the emergency services.
"There is very little time left".
"It's imperative that both governments recommit to the word, spirit and implementation of the Good Friday Agreement if there is to be any prospect of re-establishing the Executive".
"Ultimately, I think the parties understand people voted in the March Assembly elections for a strong voice at Stormont".
The unionists have struggled for years with Irish Catholic nationalists who want Northern Ireland to join a united Ireland.
The Tories need the support of the ten DUP MPs after losing their majority in last week's election disaster.
The tragic fire in a London tower block looks set to delay an agreement between Theresa May and the DUP about forming a stable government.
The talks with the DUP follow May's apology to Conservative rank-and-file lawmakers in a meeting Monday which signaled she would be more open to consultation, particularly with business leaders demanding answers about the details on Britain's departure from the European Union.
In a punchy intervention created to hike the pressure on Downing Street, he is also asking how last week's election result will affect the position on issues like Single Market membership, after days of speculation of a softer approach to Brexit from Prime Minister Theresa May.
May will also be reliant upon the 10 lawmakers from the eurosceptic DUP, who would help her edge past the 326 votes needed in parliament to avoid the government collapsing. The DUP is a traditionally Protestant party that backs keeping Northern Ireland part of the U.K. Its main rival, the pro-republican Sinn Fein, has been pushing for a referendum on Irish unity for years.
"The parliamentary arithmetic is such that we are going to have to work with everyone", he said. The European Parliament's chief Brexit negotiator Guy Verhofstadt also expressed serious concerns for the Belfast Agreement.
Scottish Conservative leader Ruth Davidson said the government should put economic growth at the heart of its Brexit strategy. That would create a "soft" border and allow companies throughout Ireland to trade with the rest of the island (and the EU) substantially as they do today.
Asked about Schaeuble's comments, Macron said the EU's door was still open for Britain as long as the negotiations were not finished, but that it would be hard to reverse course.