Kenny refuses to confirm whether Reilly will survive cabinet reshuffle
Mr Kenny insisted that all decisions made the cabinet are "collective decisions" following criticism of Dr Reilly by some ministers over his handling of the medical card issue.
He said that it is an issue that has been "brought to light over the past period", accepting that the review process has caused a "great deal of anxiety and concern".
Asked if he has full confidence in Dr Reilly, Mr Kenny replied
"I have confidence in every minister in the cabinet. Obviously the cabinet acts collectively and the cabinet make their decisions and deal with each individual issue as they come up but cabinet decisions are collective decisions.
So I have confidence in all the members of the cabinet including Minister Reilly."
But he refused to say whether Dr Reilly will remain as Health Minister following the cabinet reshuffle.
Mr Kenny said the issue of cabinet appointments is one that rests predominantly with the Taoiseach.
However, he pointed out that the Labour Party is in the process of electing a new leader and that will a baring on the make-up of the cabinet.
"It is the responsibility of the Taoiseach in terms of appointments to cabinet and so on. But clearly there is a process in train with our colleagues in government, the Labour Party, in terms of the selection of the leader they put in place," he said.
On the issue of medical cards, Mr Kenny said the panel of experts will report back on the matter by September.
"You will note today that the new panel has been appointed with specific terms of reference to report by September on the analysis of medical conditions and how people have to deal with those medical challenges might benefit in the best way from medical card coverage," he said.
I "think this is an issue that has been brought to light over the past period and it's one government are now proceeding to deal with, both in respect of the medical cards and in the analysis in the way that medical card cover is granted in the first place," he added.
Niall O'Connor Political Correspondent