WASHINGTON — Despite strong resistance from religious organizations, the Obama administration said Friday that it was moving ahead with a rule requiring most employers to provide free insurance coverage of contraceptives for women, a decision that has touched off a legal and political battle likely to rage for another year.

The final rule, issued under the new health care law, adopts a simplified version of an approach proposed by the government in February to balance the interests of women with the concerns of the Roman Catholic Church and other employers with religious objections to providing coverage for contraceptives.

After considering more than 400,000 comments, administration officials refused to budge on the basic principle. The rule, they said, is very similar to their proposal. An exemption is included for churches. But many Catholic hospitals, schools, universities and other religious institutions will have to take steps so that coverage is available to employees and their dependents.

The issue figured prominently in last year’s elections as President Obama and other Democrats pressed their advantage with female voters. At the same time, Catholic bishops waged a national campaign arguing that the federal policy infringed on religious freedom and violated the church’s social and moral teachings on birth control and abortion.