(Reuters) - The White House will announce a move to accommodate religious organizations on its rule for health insurance coverage of contraceptives, sources familiar with the matter said on Friday.

The Obama administration is seeking to quell a firestorm from Catholic Church leaders, Republicans and others who have said the regulation is an attack on religious freedom. The proposal is unlikely to satisfy church leaders, the sources said.

The proposal will aim to show flexibility toward religious organizations that have criticized the policy, but will preserve the central White House goal of ensuring that women employees of religious institutions, including schools and hospitals, receive full coverage of contraceptives in health insurances plans.

The administration has been looking at several state laws that let religious employers opt out of covering birth control in their insurance packages, so long as they refer women to a provider that will offer the benefit at low cost.

The proposed deal was first reported by ABC News.

Archbishop of Washington Cardinal Donald Wuerl, reacting to reports of the announcement, told MSNBC he was still concerned about religious rights.

Our concern is our basic freedom, and I'm not sure it makes sense to say 'how if about we compromise away parts of your freedom, how about if this part's acceptable to us and this part isn't.' I would want to see exactly what we're being offered, he said on MSNBC's Morning Joe.

Several prominent Catholic leaders have indicated in recent days that they are in no mood to compromise and will not accept anything short of the Obama administration withdrawing the regulation, which was finalized last month and is part of the administration's 2010 healthcare overhaul.

(Additional reporting by Susan Heavey and Vicki Allen.)