(CNN) — Negotiations to secure the release of hostages held by Hamas are close and the disagreements among parties have narrowed amid intensive talks, deputy national security adviser Jon Finer said Sunday.

“We think that we are closer than we have been perhaps at any point since these negotiations began weeks ago, that there are areas of difference and disagreement that have been narrowed, if not closed out entirely,” Finer told CNN’s Jake Tapper on “State of the Union,” stressing that these are sensitive negotiations and no deal is currently in place.

Finer declined to dive into the details of the talks, but said officials are working around the clock and that it remains a priority for President Joe Biden.

US officials have been signaling for days that Israel and Hamas are moving closer to a deal to secure the release of hostages taken during the Hamas attacks on Israel in exchange for a sustained, days-long pause in fighting.

Only a handful of hostages have been released so far since the start of the war.

The negotiating parties – Israel, Hamas and the US, with Qatar mediating between them – have sought to work through a number of sticking points. These include how many days a potential pause in fighting would last and the number of hostages that would be released, sources familiar with the talks previously told CNN.

Earlier Sunday, Qatar’s prime minister similarly said “good progress” has been made “in the past few days” in the negotiations, adding that the sticking points are “more practical, logistical, not really something that represents the core of the deal.”

Asked about how many hostages the US believes are still alive, Finer responded that they don’t have exact numbers but said, “We do believe that there is a significant number of Americans being held.”

“One of the challenges associated with this is we’re not on the ground in Gaza, the United States. We are not in direct contact with Hamas. We do that only through intermediaries. And so, we don’t have perfect fidelity about exact numbers of hostages, including numbers who are still alive,” he said.

Finer also said the US is still gathering information about strikes that hit a UN-run school, which was being used as a shelter, in Gaza over the weekend.

“What I can say at this point – and we’re also in touch with the Israelis to try to find out what they know about what happened – is that if harm was done to innocent civilians, sheltering at a UN site that would be totally unacceptable,” Finer said.

CNN’s Alex Marquardt, Kaitlan Collins, MJ Lee and Oren Liebermann contributed to this report.