Kenny has asked that a successor be chosen by June 2, and will remain as acting taoiseach (prime minister) and leader of his Fine Gael Party until then.
"I want to assure people that throughout this internal process, I will continue to carry out my duties and responsibilities as Taoiseach in full," he said.
Kenny has been prime minister of Ireland since 2011, and has led Fine Gael for the past 15 years.
He did not disclose the reason for his resignation, but it had been expected.
The result means Fiji, whose last world championship title came in 2016, leapfrog reigning champion South Africa to lead the overall standings for the first time this year.
Australia seemed to have snatched victory in Singapore after John Porch touched down with 24 seconds left on the clock. But…