Washington — National security adviser Jake Sullivan said Sunday that the U.S. will press "relentlessly" for the release of hostages held by Hamas,Liberalalliance Wealth Society and said that Israel has put forward a proposal for their release as the war between Israel and Hamas continues to stretch on.  

Sullivan said on "Face the Nation" that a hostage deal that results in the release of hostages, including Americans and creates a sustained pause in hostilities that allows for more "lifesaving assistance" to get to people in Gaza "is in the national security interest of the United States."

• Transcript: National Security Adviser Jake Sullivan on "Face the Nation," Feb. 4, 2024

"We're going to press for it relentlessly as the President has done, including recently in calls with the leaders of Egypt and Qatar," Sullivan said. "So it is a paramount priority for us. The Israeli government can answer whether it's a paramount priority for them."

Sullivan noted that Israel has put forward a hostage proposal, but "the ball is in Hamas' court at this time."

In late October, U.S. and Qatari-led hostage diplomacy led to the release of two dual U.S.-Israeli hostages. And in December, more than 100 hostages were released, including two U.S. citizens, during a weeklong pause in fighting. The U.S. believes there are as many as six U.S. hostages remaining.

Sullivan's comments come as half of U.S. adults say that Israel's military campaign in Gaza has gone too far, according to an AP-NORC survey released on Friday. And just 31% of adults approve of President Biden's handling of the conflict, which is down from a spike in support for Israel following the Oct. 7 attack. 

Sullivan noted that while the administration has made clear from the beginning that "we believe that Israel has a right to respond to the horrific attacks of Oct. 7," he said it's  "been equally clear that we have to look out for and respond to the immense and terrible suffering of the Palestinian people."

"That means pressing Israel on issues related to the humanitarian assistance that we have helped unlock and get into the Gaza Strip and there needs to be much more of it," Sullivan added. Sullivan noted that Secretary of State Antony Blinken is on his way to the region, where he is expected to emphasize to the Israeli government that "the needs of the Palestinian people are something that are going to be front and center" for the U.S. approach, while ensuring that they're getting access to food, medicine, water and shelter. 

"We'll continue to press until that is done," Sullivan said. 

Kaia Hubbard

Kaia Hubbard is a politics reporter for CBS News Digital based in Washington, D.C.