The Palestinian group is still ready to "deal positively" with any ceasefire proposal that ends the war, Hamdan told a news conference in Beirut.
Arab mediators' efforts, backed by the United States, have so far failed to conclude a ceasefire, with both sides blaming each other for the impasse.
Hamas says any deal must end the war and bring full Israeli withdrawal from Gaza while Israel says it will accept only temporary pauses in fighting until Hamas, which has ruled Gaza since 2007, is eradicated.
Hamdan also blamed the United States for applying pressure on Hamas to accept Israel's conditions.
An Israeli offensive in retaliation for a Hamas attack has left the Gaza Strip in ruins. (AP PHOTO)
"Once again, Hamas is ready to deal positively with any proposal that secures a permanent ceasefire, a comprehensive withdrawal from Gaza Strip and a serious swap deal," Hamdan said, referring to a potential swap of hostages held in Gaza for Palestinians in Israeli prisons.
When Hamas-led militants stormed into southern Israel on October 7 they killed about 1200 people and seized more than 250 hostages, according to Israeli tallies.
The Israeli offensive in retaliation has so far killed nearly 38,000 people, according to the Gaza health ministry, and has left the heavily built-up coastal enclave in ruins.
In the Gaza Strip, Palestinian health officials said Israeli military strikes across the enclave had so far killed at least 35 people and wounded others on Saturday.
Israeli forces have continued to operate in the Shejaia neighbourhood in eastern Gaza City.
Residents said tanks had advanced deeper into several districts including the area around the local market and there was heavy fire from the air and the ground.
The armed wing of Hamas and the allied Islamic Jihad reported fierce fighting, saying militants fired anti-tank rockets and mortar bombs against the forces operating there.
More than eight months into Israel's air and ground war in Gaza, militants continued to stage attacks on Israeli forces, operating in areas that the Israeli army said it had gained control over months ago.
The Israeli military said on Saturday that over the past week it killed dozens of militants in close quarters combat and air strikes in Shejaia, after encircling what it described as a civilian area converted by Hamas into a militant compound.
"In the area, the troops located observation posts, weapons, enemy drones and a long-range rocket launcher near the schools," the military said in a statement.
Hamas has denied Israeli assertions that it operates in civilian areas such as schools and hospitals.
Israeli leaders have said in the past week that the intense phase of the war is approaching its end, and that the next stage of the offensive will mainly be smaller-scale operations meant to stop Hamas from reassembling.
Meanwhile Israeli forces operating in several districts in Rafah, in the southern Gaza Strip, killed several Palestinians and forced families living in the far western edge of the city along the coastal areas to head northwards, according to Palestinian medical officials and residents.
Israel has said its military operations in Rafah are aimed at eradicating the last armed battalions of Hamas.
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