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.
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Two neighbouring Tube lines are to be partly suspended into a second day amid safety concerns of debris falling on to the tracks. British officials have ordered a review of other buildings that have had similar renovations.
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.
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But public anger has been swelling, with furious residents heckling May and storming the local authority headquarters on Friday. Some 19 patients are still being treated in hospital, of whom 10 are in a critical condition, the National Health Service said.
"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.
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