In both meetings, all leaders agreed on the urgent need to re-establish the Northern Ireland Executive, believing that the June 29 deadline for completing negotiations could be met, according a statement from the Irish government.
She is seeking to negotiate a so-called "confidence and supply" arrangement whereby the DUP will throw their weight behind the government in key Commons votes, such as on the Queen's Speech and Budgets.
Former Prime Minister Sir John Major has urged Theresa May to reconsider her approach, saying a deal with the DUP could threaten the Northern Ireland peace process and "carry baggage" for his party.
But she added: "On reaching such an agreement we will make sure that the details of that are made public so that people can see exactly what that is based on".
Speaking in Downing Street alongside Mr Varadka, Mrs May dismissed these concerns as she claimed her government "remains absolutely steadfast" in its commitment to upholding the Good Friday Agreement.
Dodgers' rookie Cody Bellinger becomes fastest to 21 HR-mark
To put that in perspective, Kershaw had allowed only four earned runs in his previous three starts combined. Robert Gsellman gets the start for the Mets on Tuesday opposite RHP Brandon McCarthy for the Boys in Blue.
The remarks came after warnings by the nationalist Sinn Fein and SDLP and the cross-community Alliance Party that a deal with the DUP would undermine the Government's attempts to restore the powersharing executive at Stormont.
Turning to the talks between the pair, Mr Varadkar - who has only been in his post for five days - said he had been concerned about the Tory DUP deal.
"I will be making that case tomorrow for example despite the fact that it should really be a First Minister and a Deputy First Minister there to meet Michel Barnier or others to make the case for Northern Ireland".
"We think it is very important that Northern Ireland should have a unique voice at this very important time", he said.
Theresa May has said she is "getting on with the job" amid continued questions over her future as Prime Minister.
Cosby team triumphant, but sex crime retrial, lawsuits loom
They said the jurors not being able to agree shows that he was innocent, which in the eyes of the law, it didn't. He also found success with his "Fat Albert" animated TV show and starred in commercials for Jell-O pudding.
"Instead, they want more money and to maintain free trade across northern and southern Ireland after Britain's exit from the EU', he declared".
Mr Varadkar said: "It does emphasise the strength and closeness of the relationship between our two countries".
The failure of the Irish Government to fulfil its obligations as a co-guarantor for the Good Friday Agreement is a national scandal, the South Antrim MLA said.
So I would suggest we become more demanding of those who are elected to take responsibility that they do so constructively.
Scattered showers to return Monday afternoon
Given the clouds and periodic rain, it won't be as hot Monday , and highs should stay in the mid/upper 80s. Showers and thunderstorms are possible Friday with a frontal boundary crossing the region.