By Padraic Halpin
DUBLIN (Reuters) - Irish Prime Minister Enda Kenny resisted a call on Monday from a lawmaker of his Fine Gael party to step down over the next two months, rejecting the first open challenge to make good on a promise to allow a change of leadership.
Kenny returned to office in May as head of a minority government that is due to run until the end of 2018. He has said he will not lead his center-right party into the next election but not specified when he will stand down.
Pressure for Kenny to announce a timeline has risen since an opinion poll last week showed his party had fallen nine percentage points behind its main rival, Fianna Fail.
"The best opportunity for the country for stable government is a change of leadership. Particularly in the context of Brexit, we need to have a stronger Fine Gael," party legislator Brendan Griffin told national broadcaster RTE on Monday.
He added that the only opportunity for "an orderly transition" was the summer parliamentary recess starting this month and running into September.
In a speech broadcast by RTE, Kenny said he had "no intention of being diverted from ... that responsibility that I've undertaken and which I have received a mandate to fulfill."
After suffering heavy losses in elections in February, Fine Gael returned to power with the backing of a group of independent lawmakers and facilitated by Fianna Fail, theoretically putting in the latter in a position to trigger a snap election.
Griffin said he was considering filing a motion of no confidence in Kenny at Fine Gael's weekly party meeting on Wednesday, but senior ministers came out in support of the prime minister.
"This is not the time for a leadership challenge. In the light of Britain's vote to leave the European Union, which is a big body blow, we need the experience of the Taoiseach (prime minister) and his relationships in Europe," Education Minister Richard Bruton, who led a challenge against Kenny in 2010, told RTE.
(Editing by Keith Weir and John Stonestreet)