DUBLIN (Reuters) - Irish Prime Minister Enda Kenny told unsettled members of his ruling Fine Gael party that he would conclusively deal with the issue of his leadership after meeting the U.S. president next month, the party’s chairman said on Wednesday.

FILE PHOTO: Irish Prime Minister Enda Kenny pauses before speaking to the media at the general election count centre in Castlebar, Ireland, February 27, 2016. REUTERS/Clodagh Kilcoyne/File Photo

Kenny - who has already said he will not lead the party into an election due as early as next year - has faced growing calls to clearly spell out his plans as support for the party slumped amid the government’s mishandling of a policing scandal.

One of the two top contenders to take over the center-right party, Simon Coveney, had said a new leader should be chosen after Kenny’s trip to Washington for the annual meeting with the U.S. president to mark St. Patrick’s Day on March 17.

“The Taoiseach (prime minister) has addressed the issue. He has told us he will outline his intentions effectively and conclusively shortly after his return from the U.S.,” Fine Gael party chairman Martin Heydon said in a statement.

Kenny stopped short of giving an exact timeline, but one source present, who asked for anonymity as the meeting was private, said there was a “clear indication” that the 20-day leadership contest would begin the week following the trip.

Fine Gael vice-chairman Pat Deering, who warned that the 65-year-old leader would face a motion of no confidence if he did not detail his plans at the meeting, said no such motion was now needed.

Kenny, prime minister since 2011 and the leader of his party for almost 15 years, is expected to hand over to a much younger colleague. While other ministers are weighing a run, the clear favorites are the 44-year old Housing Minister Coveney and 38-year-old Social Protection Minster Leo Varadkar.

Varadkar, Ireland’s first openly gay minister, has long been seen as the strongest contender to take over as prime minister. Known as a plain-speaker, supporters say he would widen the party’s appeal after it lost a quarter of its seats at parliamentary elections last year.

However Coveney, the son of a former Fine Gael minister, has firmly closed the gap after seeking his appointment to the newly established housing ministry last year, raising his profile by trying to tackle a severe housing and homelessness crisis.

“There was a perception that a lot of people in the party were leaning towards Leo when the issue wasn’t focused in people’s minds,” Fine Gael Vice-President John Paul Phelan, a Varadkar supporter, told the Irish Times on Wednesday.

“But this contest is completely up in the air in terms of numbers.”