The Taoiseach Enda Kenny raised the issue of the undocumented Irish in the US during a phone conversation with US Vice President-elect Mike Pence tonight.
US President-elect Donald Trump has repeatedly pledged that he will deport illegal immigrants once he takes office.
There are an estimated 11 million illegal immigrants in the US, including approximately 50,000 Irish people.
Irish immigration groups in the US have been trying to calm fears in the wake of Mr Trump's election.
During the Taoiseach's phone call, he congratulated Mr Pence on his recent electoral success.
Had a really good conversation tonight with US VP Elect Mike Pence. He certainly knows Ireland and the issues that matter to our people.— Enda Kenny (@EndaKennyTD) November 18, 2016
He also expressed his intention to engage positively with the new administration on a number of issues to the mutual benefit of Ireland and the US, said a statement on behalf of the Taoiseach.
Mr Kenny "raised the issue of the undocumented Irish in the US and expressed his determination to work with the President and Vice President-elect in seeking a solution to the issue," said the statement.
The Taoiseach also referred to the economic ties between the two countries during the 15-minute "warm" conversation.
He spoke about long standing and productive relationship Ireland has with many US companies, as well as the fact that there are 100,000 Americans employed in Irish companies across America, said the statement.
Both men spoke of Mr Pence's strong Irish heritage and the Taoiseach expressed the wish that Mr Pence might visit here again sometime in the future, added the statement.