"We know each other and we understand each other", she said.
The former Northern Ireland First Minister said her meeting with Mr Varadkar was very good and that she was looking forward to a very positive relationship with the Irish premier.
And they said it could cause a conflict of interest amid ongoing talks to restart the devolved administration in Northern Ireland, of which the British Government is meant to be an impartial broker. We want to get the institutions re-established.
Northern Ireland-based DUP won 10 seats.
"As a UK Government we remain absolutely steadfast in our commitment to the Belfast Agreement, its successor agreements".
Conservative Party sources say May wants to show her government is up and running but her loss of authority in last week's election will make it harder to handle a hectic agenda - Brexit talks with the European Union, tackling a slowing economy, a political crisis in Ireland, and a devastating fire in London.
The institutions collapsed amid a bitter row between the DUP and Sinn Féin about a botched green energy scheme.
He warned that a deal between the Conservatives and DUP would be in breach.
The Irish government will be critical to that and the should reassert their role as co-guarantors of our agreements.
"We will continue with those negotiations throughout the weekend and into next week", Foster said.
On the advancement of talks with the DUP, South Staffordshire MP Mr Williamson said: "Good progress is being made in discussing the substantive issues surrounding any potential agreement".
"I want us to have a good working relationship so that from his jurisdiction and my jurisdiction we can work together for the good of all our people", she added.
It has positioned itself against republican parties like Sinn Fein, which believes that Northern Ireland should be a part of the Republic of Ireland, bringing the whole island under a single government.
The Northern Irish party in talks to support Theresa May's minority government hopes to conclude negotiations with the prime minister's Conservative Party as quickly as possible, its leader told BBC on Friday.