While four of the eight judges who heard the case believe Hobby Lobby should qualify for a temporary injunction, they were one vote short of a majority.
The case has been sent back to the lower court with instructions for further review.
Hobby Lobby's lawsuit will now head back to U.S. District Court for the Western District of Oklahoma, which earlier ruled against Hobby Lobby's quest for relief from the health care law.
Beginning Monday, the company will be subject to fines of up to $1.3 million a day for failing to comply with the health care mandate.
Hobby Lobby's attorneys filed court documents Thursday afternoon in hopes of obtaining the injunction before the July 1 deadline when the fines will start to accrue.
“We are asking the court to move by all due haste,” Duncan said.
Oklahoma Attorney General Scott Pruitt, who submitted a legal brief in support of Hobby Lobby, lauded the court's ruling on Thursday, calling it a win for Oklahoma and other states that have challenged the Affordable Care Act. Insurance Commissioner John Doak also praised the ruling.
“The health care law's mandate requiring religious groups to violate their lawful beliefs and practices directly goes against the ideals that our founding fathers set in place to protect Americans from an overbearing and intrusive government,” Pruitt said in a statement.
The watchdog group Americans United for Separation of Church and State said the ruling could open the door for religious employers to deny access to certain forms of birth control to their employees.
“This is taking the direction of defining religious liberty in a disturbing way by allowing the religious beliefs of an owner of even a secular company to undermine reproductive rights of women and individual employees,” said Barry Lynn, executive director for Americans United.