Hamas officials have said the group is engaging positively with mediators but the fate of a Gaza ceasefire lies in talks between the US and Israel.
However, Israel and Hamas remain far apart on the terms of a possible truce and hostage deal in Gaza, sources said on Tuesday. US President Donald Trump's recent upbeat comments on the prospect of an agreement were premature, the sources said.
Mr Trump is expected to meet Israeli Prime Minister Benjamin Netanyahu at the White House next week to press him for an end to the war in Gaza.
"We are engaging positively with the mediators," a Beirut-based Hamas official said. "What matters to us is stopping the aggression and the massacres. We hope something positive will happen on this front.
"The problem lies with Netanyahu and his government, which does not respond to the mediators’ calls to halt the aggression, release the prisoners, allow aid into Gaza, and withdraw."
In Washington, Mr Trump is expected to tell Mr Netanyahu that the war, now more than 20 months old, can no longer continue, sources in the US said on Monday.
"Netanyahu is ready to discuss a ceasefire, because the military and political objectives of the war have long been achieved," one of the sources said.
A second Hamas official said "the Israelis and Americans are discussing matters among themselves. We are waiting for what will come out of those discussions".
"There are positive signals from the Israelis and Americans, but there is no reliance on Mr Trump given his historical positions on Hamas, which are far from promising," he added.
Mr Trump this week said a deal could be reached within a week. "Make the deal in Gaza, get the hostages back," he later wrote on Truth Social, his social media platform.
Mr Netanyahu said new opportunities had opened up for recovering the hostages held in Gaza.
"The mediators from Egypt, Qatar and the US don't see that a deal can be reached any time soon," one of the sources said. "You only need to listen to Hamas and Israeli negotiators talking about their conditions to realise that no way a deal will be reached within in a week."
Contact between Hamas and Israel on one side and mediators from Egypt, Qatar and the US on the other has increased over the past week in Cairo, with the objective of finding enough common ground to hold another round of talks, said the sources.
They said Israel, with US backing, has rigidly stood by its long-standing demands that Hamas surrender its arms and dismantle its military capabilities, including its network of underground tunnels and hardware manufacturing sites.
Hamas has categorically refused to give up its arms but signalled it was open to discuss laying down its weapons and not be part of the post-war government or reconstruction of the enclave.
It has also suggested it was prepared to agree to a demand that its leaders leave Gaza to live in exile abroad but only on condition that Israel does not target them.
Israel, said the sources, has meanwhile been threatening to pursue Hamas leaders in Gaza if the group does not accept a temporary ceasefire during which it releases the remaining hostages.
"Israel and the US have made it clear they don't want another Lebanon in Gaza," said another source, alluding to decades of the Iranian-backed Hezbollah operating in that Arab country as a "resistance" group outside state authority.
"Hamas is in a tenuous position. It has lost much in this war, with its top-tier military and political leaders eliminated. Yet it continues to try to maintain a presence in Gaza as a resistance group fighting an illegal occupation."
Under discussion is a 60-day truce during which Hamas is expected to release 10 living hostages and half the remains of others who died in captivity. In return, Israel is expected to free hundreds of Palestinians detained in Israeli prisons.
Of the estimated 50 hostages Hamas still holds, only 20 are believed to be alive, according to Israel's military.
The proposal also includes the resumption of humanitarian assistance into Gaza and the start of Hamas-Israel negotiations on an Israeli withdrawal from Gaza and an end to the war.
Hamas wants the US to guarantee that these negotiations continue until Israel pulls out and ends the hostilities.
The war in Gaza started after a Hamas-led attack on October 7, 2023, that killed about 1,200 people, according to Israeli figures. Israel's retaliatory campaign has killed more than 56,600 Palestinians in Gaza and reduced most of the coastal strip to rubble.
Humanitarian conditions for the more than two million people there have been worsening amid Israeli restrictions on the entry of food aid and supplies.
