The Green family filed suit in September, saying the law would force them to "to violate their deeply held religious beliefs under threat of heavy fines, penalties and lawsuits." It claims the mandate is unconstitutional.
Duncan said the company has no objection to other forms of birth control and includes them in its insurance plan.
"Hobby Lobby ought to be able to get a narrow exemption," Duncan said.
Hobby Lobby calls itself a "biblically founded business" and is closed on Sundays, provides spiritual counseling for its employees and does not sell products that are inconsistent with its owners' religion. Founded in 1972, the company now operates more than 500 stores in 41 states and employs more than 13,000 full-time employees who are eligible for health insurance coverage.
The lawsuit also was filed on behalf of Mardel Inc., another of the family's businesses. The bookstore and education company, also based in Oklahoma City, sells a variety of Christian-themed materials. It operates 35 stores in seven states and has 372 full-time employees.
In a separate case involving a Detroit-area company owned by Roman Catholics, Weingartz Supply Co. on Wednesday won an early round in its lawsuit challenging the health care law's mandate requiring contraception coverage. A federal judge blocked the government from taking any action against that company, which sells outdoor power equipment. The company is challenging the contraception mandate on religious grounds.