Carter told the Senate Armed Services Committee that the U.S. "won't hold back" from supporting partners carrying out such attacks or from "conducting such missions directly, whether by strikes from the air or direct action on the ground."
The White House, however, has yet to make a decision on the options for upping the campaign against ISIS, according to defense and administration sources. They said that further involvement on the ground was one of the possibilities being presented.
The ground option Carter mentioned to the committee was part of a three-prong effort -- which he dubbed the "three Rs" -- to adapt the U.S. policy on countering ISIS.
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In addition to increased ground action and airstrikes, or "raids," Carter also spoke of the need to increase pressure around the ISIS stronghold of Raqqa in Syria, where "we will support moderate Syrian forces" fighting the terror organization there.
The last "R" is Ramadi, the capital of Iraq's Anbar province, where Carter said the U.S. would do more in terms of providing assistance and fire support to local Iraqi forces to take on ISIS.
But several GOP senators blasted what they heard from Carter and Joint Chiefs of Staff Chairman Joseph Dunford, who also testified Tuesday.
"This is a half-assed strategy at best," South Carolina Sen. Lindsey Graham, a Republican presidential candidate, said after a lengthy back-and-forth with Carter about how the U.S. is supporting fighters in Syria.
The U.S. earlier this month announced it was pausing its costly program to train and equip Syrian rebels that has resulted in limited gains, focusing instead on supplying military aid to opposition leaders.
Graham and committee Chairman John McCain of Arizona peppered Carter with questions about how the U.S. would protect forces as Russia carries out airstrikes that have been hitting forces opposed to Syrian President Bashar al-Assad.
"Are we going to protect them from being barrel bombed by Bashar Assad and protected from Russia?" McCain asked.
"We have an obligation to do that. We made that clear right from the beginning of the train-and-equip program," Carter said.
"We haven't done it. We haven't done it," McCain disagreed.
Carter said to date, no forces that have been part of the U.S. training program have come under attack from Russian forces, but McCain once again disagreed.
"I promise you they have," McCain said. "You will have to correct the record. ... These are American-supported and coalition-supported men who are going in and being slaughtered."
Graham also drilled down on the new strategy, including whether U.S.-trained forces will continue to have the administration's support if they begin to fight Assad and not just ISIS.
One of the principal criticisms of the administration's train-and-equip plan has been that it only supports Syrian rebels in their fight against terrorism, but with the nation in the throes of a civil war, those rebels largely also want to take out Assad.
Assad's regime is supported by Russia, and U.S. officials have said that Moscow's military intervention in Syria appears more focused on protecting Assad than stopping ISIS.
"If I'm Assad, this is a good day for me, because the American government has just said, without saying it, that they're not going to fight to replace me. The Russians and the Iranians and Hezbollah, this is a really good day for them because their guy has no military credible threat," Graham said.