Irish Prime Minister Enda Kenny arrives at the EU summit in Brussels, Belgium, March 9, 2017. REUTERS/Dylan Martinez

DUBLIN (Reuters) - Irish Prime Minister Enda Kenny said on Tuesday he will attend a meeting of European Union leaders on April 29 for Brexit talks, keeping his party guessing on when he intends to step down.

Kenny came under pressure to name a date for his planned departure last month after his handling of a crisis in the Irish police force threatened to bring the government down.

He told members of his ruling Fine Gael party a month ago that he would “conclusively deal” with the issue of his leadership after meeting the U.S. president on March 17.

Yet on Tuesday Kenny did not say whether he would be prime minister when negotiations on Britain’s exit from the European Union get under way in late May or early June.

“I do expect to attend on April 29 at the European Council meeting,” Kenny told parliament as opposition lawmakers demanded to know who would be in charge of the country when negotiations take place - a critical event for Ireland given its close ties to Britain.

Kenny has already said he will not lead the party into a parliamentary election due as early as next year.

But while some Fine Gael members had expected that the 20-day party leadership contest would begin this week, finance minister Michael Noonan suggested on Monday that Kenny should stay on until the end of May or early June.

Kenny, prime minister since 2011 and the leader of his party for almost 15 years, is expected to be replaced by a younger colleague - most likely Social Protection Minister Leo Varadkar or Housing Minister Simon Coveney.

Whoever wins will be both party leader and prime minister at least until the election. Fine Gael is laboring in most opinion polls behind rivals Fianna Fail.