US President-elect Donald Trump's Middle East envoy, Steven Witkoff, said that returning Israeli prisoners held in Gaza is the "most important thing" for him before his inauguration on January 20.

"Reaching an agreement to release the hostages is the most important thing for President Trump before the inauguration," Witkov told Israel's Channel 12 on Thursday.

He continued: "President Trump personally directed me to exert maximum pressure to move forward with the agreement."

The Israeli channel indicated that Witkov is expected to visit the Qatari capital, Doha, in the coming days as part of the intensive efforts to reach an agreement.

The channel quoted unnamed American sources as saying that "there is close and unusual cooperation between the outgoing Biden administration and the incoming Trump team."

"Biden administration officials confirmed that there was full coordination between the two parties, as Brett McGurk, Biden's representative, remained in constant contact with Witkoff," she said.

According to the channel, "a development was noted in the talks when Hamas agreed to accept the list of 34 kidnapped men presented by Israel, and expressed its readiness to release the living kidnapped men from the list, including men under the age of 50 who were defined as being in a humanitarian situation."

On Sunday evening, a Hamas official said that the movement had agreed to a list of 34 Israeli prisoners submitted by Tel Aviv to be exchanged for Palestinian prisoners as part of a possible ceasefire agreement in Gaza.

The prisoner exchange negotiations, mediated by Qatar, Egypt and the United States, have stumbled more than once, due to Netanyahu’s insistence on maintaining control over the Philadelphi Corridor on the border between Gaza and Egypt, and the Rafah crossing in Gaza, and preventing the return of Palestinian faction fighters to northern Gaza by searching returnees through the Netzarim corridor in the middle of the Strip.

For its part, Hamas insists on a complete Israeli withdrawal from the Gaza Strip and a complete cessation of war, in order to accept any agreement.

Tel Aviv is holding more than 10,300 Palestinians in its prisons, while it estimates that there are 100 Israeli prisoners in the Gaza Strip, while Hamas announced the killing of dozens of its prisoners in random Israeli raids.