The White House is working to reach a hostage deal between Israel and Hamas before president-elect Trump’s inauguration, William Burns, the director of the CIA, has suggested.

“Negotiations going on right now are quite serious and do offer the possibility, at least, of getting this done in the next couple of weeks,” Burns said in an interview with National Public Radio on Friday. “This administration worked very hard at that right up until 20 January. I think the coordination with the new administration on this issue has been good. President-elect Trump has made clear his interest in trying to get a deal, you know, before his inauguration.”

The CIA director’s interview with Mary Louise Kelley on NPR’s All Things Considered took place as Israel and Hamas appeared to be edging closer towards a ceasefire and hostage release deal that could bring the bloodshed in the Gaza Strip to an end amid reports of optimism among decision-makers.

Hamas said on Monday that it had given mediators a list of 34 Israeli captives who were seized during the group’s attack on Israel on 7 October 2023 that triggered the war, and who could be freed as part of the “first phase of a prisoner exchange deal”.

The list included the remaining women, children and older and injured people, Hamas said, although Israel said the militant group had yet to convey whether those named were alive or dead.

“I’ve learned the hard way not to get my hopes up about the ceasefire hostage negotiations,” Burns said. “I do think there remains a chance to get a deal. The gaps between the parties have narrowed.”

Several rounds of talks mediated by the US, Egypt and Qatar have failed to produce a lasting ceasefire. Officials have repeatedly voiced optimism that a breakthrough was close only for the negotiations to founder.

Hamas insists that any negotiations to secure the release of hostages must form part of a comprehensive pact to end the hostilities in Gaza, while the Israeli prime minister, Benjamin Netanyahu, is seeking a more segmented agreement, aiming for a deal that would see the liberation of some, though not all, hostages, while simultaneously preserving Israel’s prerogative to recommence hostilities against Hamas upon the deal’s expiration.

In recent weeks, the issue of the hostages and a ceasefire agreement have been at the heart of an intense debate in the Israeli media. Critics accuse Netanyahu of deliberately stalling the deal, ostensibly to await Trump’s assumption of office.

Western intelligence services estimate that at least one-third of the remaining 95 or so Israeli captives in Gaza have been killed. Despite the latest talks, Israel has stepped up airstrikes on the Palestinian territory that killed at least 100 people last weekend, local health officials said.

The Israeli newspaper Haaretz reported that Netanyahu “is betting that Trump’s pressure campaign will bring Hamas to its knees”, but noting how “the prime minister has been wrong many times before about the impact of different events on the group’s negotiating positions”.

Kobi Michael, a senior researcher at the Israeli thinktank the Misgav Institute for National Security and Zionist Strategy, told Agence-France Presse earlier this week: “I cannot foresee significant progress until President Trump assumes office.”

Trump’s return to office could prove advantageous for Netanyahu’s expansionist policies, particularly regarding settlement expansion and potential annexation in the West Bank.

Trump has said there will be “hell to pay” if Hamas does not release its hostages before he takes office, suggesting he is seeking a deal before the inauguration day.

On Friday, the mediator Qatar said had it briefed Trump’s Middle East envoy, Steve Witkoff, about the Gaza ceasefire talks.

In their meeting in Doha, the Qatari prime minister, Sheikh Mohammed bin Abdulrahman Al Thani, and Witkoff discussed “the latest developments in the region, especially the efforts aimed at reaching a ceasefire in the Gaza Strip”, the Qatari foreign ministry said.

Conditions in Gaza, where almost all of the population on 2.3 million are living in makeshift accommodation, are deteriorating in the face of cold and wet winter weather, which has caused flooding.

Israel’s offensive in Gaza has killed at least 46,537 Palestinians and wounded 109,571 since 7 October 2023, the Palestinian territory’s health ministry said on Saturday. About 1,200 Israelis were killed and 250 taken hostage in the Hamas attack.