The prime minister of the United Kingdom on Monday reassured her Irish counterpart that her country's withdrawal from the European Union would not diminish the relationship between the two island nations.

Theresa May met with the newly-elected Irish Taoiseach (prime minister in the Irish language, Gaelic), Leo Varadkar, at 10 Downing Street in London.

"We're leaving the European Union but we're not leaving Europe, and we want to remain committed partners and allies of Ireland," May said at the joint press conference following the meeting.

She added that she was committed to making sure the "unique" relationship between London and Dublin continued as Brexit negotiations were kick-started Monday in Brussels.

"It's more important than ever that the relationship between our countries continues to go from strength to strength," May said.

She pointed out that trade between the countries was worth over 43 billion pounds ($54.8 billion) a year and supported 400,000 jobs.

May also vowed to find a practical solution that recognized the "unique economic, social, cultural and political context" of the shared land border between Northern Ireland and the Republic, with a priority being to ensure a border as frictionless and seamless as possible.

Meanwhile, Varadkar said he had expressed his concerns to May about the forthcoming deal between Northern Ireland's Democratic Unionist Party and the UK's Conservative Party to prop up May's minority government following the recent snap elections.

The Taoiseach _ a Christian Democrat of Indian heritage who took office last Wednesday and became Ireland's first openly gay head of government _ added that, after speaking with May, he was "very reassured."

On the border question, Varadkar said that it should be a political border and not an economic one, while "any border that does exist should be invisible."

Both leaders expressed their hope that the parties in Northern Ireland would be able to meet the June 29 deadline for talks to establish their power-sharing arrangement for the devolved government at Stormont.

Varadkar said that the country needed an Executive that would speak for both communities (Catholics and Protestants).