(AP) — Nebraska has abandoned its initial attempt to block part a new federal health care rule that requires church-affiliated employers to cover birth control for employees, but is vowing to continue the fight.

The Nebraska Attorney General’s Office has dropped its appeal of a federal judge’s dismissal last year of a lawsuit challenging the new law. Shannon Kingery, spokeswoman for Attorney General Jon Bruning, says the attorney general’s office is exploring the best way to challenge the law.

Bruning and several other Republican state attorneys general sued in early 2012 to try to block the law, saying the rule violated the rights of employers that object to the use of contraceptives on religious grounds. A federal judge dismissed the lawsuit in July 2012.