Hamas said on Tuesday that an Israeli proposal on a ceasefire in Gaza met none of its demands.
The proposal was delivered to Hamas by Egyptian and Qatari mediators at talks in Cairo aimed at finding a way out of the devastating war in the Palestinian enclave, now in its seventh month.
Israeli forces meanwhile stepped up bombardments on Deir Al-Balah and Rafah in central and southern Gaza Strip on Tuesday, two areas they have not so far invaded, medics and residents said.
An airstrike killed a municipal chief in Al-Maghazi refugee camp in central Gaza, Hamas said. Israel said he was a military officer.
The talks in Cairo, also attended by the director of the US Central Intelligence Agency William Burns, have so far failed to reach a breakthrough towards pausing the war.
Hamas said on Tuesday a new Israeli proposal failed to meet its demands.
"The movement (Hamas) is interested in reaching an agreement that puts an end to the aggression on our people, despite that the Israeli position remains intransigent and it didn't meet any of the demands of our people and our resistance," Hamas said in a statement.
However, it said it would study the proposal further and deliver its response to the mediators.
Hamas officials had told Reuters on Monday that the group has rejected the Israeli ceasefire proposal and that no progress had been made at the talks.
Hamas wants any agreement to secure an end to the Israeli military offensive, a withdrawal of Israeli forces from Gaza, and to allow displaced people to return to their homes across the enclave.
Israel wants to secure the release of hostages seized by Hamas in the October 7 cross-border raid that triggered the conflict and to neutralise Hamas - which rules Gaza - as a threat.
It has said it is keen to reach a prisoners-for-hostages deal by which it would free a number of Palestinians jailed in its prisons in return for the hostages in Gaza, but it was not ready to end the military offensive.