Senior Hamas official Bassem Naim told Reuters the group had presented its proposal for a ceasefire agreement to the mediators during two days of talks, and was now waiting for a response from the Israelis, who stayed away from this round.
"(Prime Minister Benjamin) Netanyahu doesn't want to reach an agreement and the ball now is in the Americans' court" to press him for a deal, Naim said.
Israel has declined to comment publicly on the talks in Cairo.
A source told Reuters earlier that Israel was staying away because Hamas had rejected its demand to furnish a list of all hostages who are still alive. Naim said this was impossible without a ceasefire first as hostages were scattered across the war zone and held by separate groups.
The Cairo talks had been billed as a final hurdle to reach the war's first extended ceasefire - a 40-day truce during which dozens of hostages would be freed and aid would be pumped into Gaza to stave off a manmade famine, ahead of Ramadan, which is due to begin at the start of next week.
Egyptian security sources said on Monday they were still in touch with the Israelis to allow the negotiations to continue without an Israeli delegation present.
Washington, which is both Israel's closest ally and a sponsor of the ceasefire talks, has said an Israeli-approved deal is already on the table and it is up to Hamas to accept it. Hamas disputes this account as an attempt to deflect blame from Israel if the talks collapse with no deal.
The United States has also called on Israel to do more to alleviate the humanitarian catastrophe in Gaza, where more than 30,000 people have been killed by Israel's assault, launched after Hamas attacks that killed 1,200 people in October.
HUNGER STALKS GAZA
Famine is now gripping the besieged Gaza Strip as aid supplies, already sharply curtailed since the start of the war, have dwindled to barely a trickle over the past month. Whole swathes of the territory are completely cut off from food. Gaza's few functioning hospitals, already overwhelmed by the wounded, are now filling with children starving to death.
Ahmed Cannan, a toddler with sunken eyes and an emaciated face, lay on a bed at Al-Awda clinic in Rafah, wrapped in a yellow cardigan. He had lost half his weight since the start of the war and now weighs just 6 kg (13 pounds).
"His situation worsens each day. God protect us from what is coming," his aunt, Israa Kalakh, told Reuters.
Nurse Diaa Al-Shaer said such emaciated children were now pouring into the clinic in unprecedented numbers: "We will face a large number of patients who suffer from this, which is malnutrition," she said.
The situation is worst in the north of Gaza, beyond the reach of aid agencies or news cameras. Gaza health authorities say 15 children have died of malnutrition or dehydration at one hospital.
Israel says it is willing to allow in more aid to Gaza through the two checkpoints on the southern edge of the territory it has permitted to open, and blames UN and other aid agencies for failing to distribute it more widely.
The aid agencies say this has become impossible with a breakdown of law and order, and it is up to Israel, whose troops have stormed Gaza's towns and patrol them, to provide access and security for food distribution.
"The sense of helplessness and despair among parents and doctors in realising that lifesaving aid, just a few kilometres away, is being kept out of reach, must be unbearable," said Adele Khodr, UNICEF regional director for the Middle East and North Africa.
