The spouses of gay and lesbian service members will be among those to receive federal benefits, including burial at Arlington National Cemetery, the Pentagon announced Wednesday, hours after the Supreme Court overturned the 1996 Defense of Marriage Act.

The Defense Department does not, however, yet know how much these benefits will cost, how it will pay for them or whether they will all extend to service members in states that do not allow gay marriage.

"We will move very swiftly, expeditiously, on implementing the law," Defense Secretary Chuck Hagel said during a Wednesday afternoon press briefing. "We think it's the right decision."

When asked how much it will cost the department, currently roiled by budget cuts and sequestration, Hagel said, "we just received the decision. We are now of course exploring all the pieces."

"I haven't had more than two hours," he added. "I read the basic opinion. I haven't talked to any lawyers about it."

"I have a responsibility to carry out the law of the land – the decision the Supreme Court gave today – from this place," he said.

In a statement released shortly after the Supreme Court decision, Hagel, a former U.S. senator from Nebraska, said the department "welcomes the Supreme Court's decision" and stated it "intends to make the same benefits available to all military spouses – regardless of sexual orientation – as soon as possible." Hagel's tenure in the Senate began in 1997 so he did not vote on the original DOMA bill.

The department will immediately start updating the process for issuing identification cards for military members and their spouses in accordance with this shift in federal policy. This will take between six and 12 weeks, according to a Defense release.

Benefits that same-sex spouses will enjoy include medical, dental, and housing and also the right to be interred at Arlington National Cemetery in Virginia.

Army Gen. Martin Dempsey, chairman of the Joint Chiefs of Staff, was visibly cooler in his response to the policy shift.

"The Joint Chiefs have made it very clear that we will follow the law of the land. The law of the land has changed, so we will assess as quickly as possible what that means," he said at the briefing with Hagel.

Dempsey said the military is sometimes construed as resistant to these kinds of policy shifts.

"We actually have done what I think is a very credible job of ensuring as much equality as we are able to provide," he said. "We will do that when we can for [gay service members and their spouses] within the limits of the law."

Some veterans groups, including the Iraq and Afghanistan Veterans of America, expressed their enthusiasm for the Supreme Court's ruling.

"Today's decision is in fact a victory for the strength of our armed forces," said Derek Bennet, IAVA chief of staff. "Support for military families is one of the most critical elements of a strong and healthy fighting force. IAVA is proud that all American service members can now serve openly in the military, and that they and their families can receive the benefits that they have earned."