But as he prepared to attend Fine Gael’s pre-Dáil think-in in Newbridge, Kildare, Mr Kenny warned the Government could not be held to ransom on a weekly basis.
Mr Halligan’s comments come as speculation on whether he will resign over a refusal to fund a second specialist cardiac lab for the South East continues.
A clinical review has recommended improving staffing levels and equipment, but said there is no need for a second lab for the region.
Mr Halligan claims government ministers reneged on a vow to fund a second lab at Waterford Hospital.
In a highly inflammatory interview over the weekend, the Independent Alliance minister also said he would “bring all hell down” on the Government if the lab is not delivered. He accused Fine Gael ministers of employing “dirty politics”.
Mr Kenny said he did not condone the interview. He called on Mr Halligan to devote himself to his responsibilities in government, including the 11 areas of his education and jobs portfolio.
But, speaking to Newstalk, Mr Kenny warned that there cannot be a situation where every week the Government is “held to ransom”.
The Independent Alliance will meet this week to discuss budget preparations but Mr Halligan’s position will also be discussed with him.
Arriving at his party’s meeting, Mr Kenny dodged questions about whether he had “confidence” in his embattled minister.
In a poignant remark, he also warned that he was the person who had the power to “appoint and dismiss” government officials. It was “his [Mr Halligan’s] decision” whether he resigned or not, he said.
Mr Kenny also said he would assess the performance of ministers next year.
Fine Gael sources confirmed there is active consideration being given to Mr Halligan’s replacement if he resigns.