In the Dáil today, Mr Kenny said the issue was not a funding problem, rather it was about the inability to attract enough doctors here.
He was responding to questions from Sinn Féin leader Gerry Adams who asked for a list of hospitals that would be affected.
The Taoiseach said he could not provide that exact information at this time and said the Health Minister is working intensely on resolving the issue.
Meanwhile, Minister for Health Dr James Reilly has said some Emergency Departments will struggle to fill junior doctor posts from next month.
Hospitals across the country may have to curtail services due to a chronic shortage of non-consultant hospital doctors after 11 July - the date when doctors are rotated between posts as part of their training.
The shortages are occurring despite a record number of doctors qualifying in Ireland.
Speaking on RTÉ's Frontline programme last night, the minister said efforts are being made to address the problem, but smaller hospitals will struggle.
