Israel ramped up its attacks on southern Gaza's Rafah on Thursday amid waning hopes for a prolonged cease-fire in the besieged Palestinian territory.

Israeli forces bombed areas in the southern border city, where more than half of Gaza's population is sheltering.

The renewed attacks come a day after Prime Minister Benjamin Netanyahu rejected a proposal to end the brutal war.

Netanyahu said Wednesday terms proposed by Hamas for a cease-fire, which would also involve releasing hostages held by the Palestinian resistance group, were "delusional" and vowed to fight on, saying victory was in reach and just months away.

The rejection followed intense diplomacy to end the monthslong conflict before a threatened Israeli assault on Rafah, which is now home to over a million people, many of them in makeshift tents and lacking food and medicine.

Aid agencies have warned of a humanitarian catastrophe if Israel follows through on its threat to enter one of the last remaining areas of the Gaza Strip that its troops have not moved into during its ground offensive.

U.N. Secretary-General Antonio Guterres said Wednesday that pushing into Rafah on the border with Egypt would "increase what is already a humanitarian nightmare with untold regional consequences."

Israel says it takes steps to avoid civilian casualties and accuses Hamas members of hiding among civilians, including at school shelters and hospitals, leading to more civilian deaths. Hamas has denied this.

Israeli planes bombed areas in Rafah on Thursday morning, residents said, killing at least 11 people in strikes on two houses. Tanks also shelled some areas in eastern Rafah, intensifying the residents' fears of an imminent ground assault.

"We have our backs to the (border) fence and faces toward the Mediterranean. Where should we go?" said Emad, 55, a displaced person who is a father of six.

"There is no place to go. One million people and more than 1 million are asking this question today; where shall we go?" Emad told Reuters via a chat app.

Diplomatic push

Despite Israel's rejection of the Hamas proposal, more talks are planned and U.S. Secretary of State Antony Blinken, on his fifth trip to the region since the start of the war, said he saw room for further negotiation.

In a late-night press conference in a Tel Aviv hotel on Wednesday, Blinken said elements of the proposal put forward by Hamas had contained clear "non-starters," without saying what they were.

"But we also see space in what came back to pursue negotiations, to see if we can get to an agreement. That's what we intend to do," he said.

A Hamas delegation led by senior official Khalil al-Hayya arrived in Cairo on Thursday for cease-fire talks with Egypt and Qatar, the mediators in the latest diplomatic push.

The delegation is expected to meet Egyptian intelligence chief Abbas Kamel and the team managing Egypt's mediation on Gaza, Egyptian security sources said.

Speaking in Nicosia, Egyptian Foreign Minister Sameh Shoukry said Egypt was working with all stakeholders to find a solution to end the conflict and urged the international community to apply more pressure to allow aid into Gaza.

"The human suffering in Gaza is unthinkable, and a humanitarian support system on the verge of collapsing, and the threats of a dangerous expansion of the conflict are real and unfolding," he told reporters.

Jordan's King Abdullah has also embarked on a diplomatic mission aimed at ending the war, visiting Western capitals in a tour that will include a meeting with U.S. President Joe Biden.

Hamas, which governs Gaza, proposed a cease-fire of 4 1/2 months, during which all hostages held in Gaza would go free, Israel would withdraw its troops from Gaza and an agreement would be reached on an end to the war.

The Hamas offer was a response to a proposal drawn up by U.S. and Israeli spy chiefs and delivered to Hamas last week by Qatari and Egyptian mediators.

Israel would be willing to let Hamas military leader Yahya Sinwar go into exile in exchange for the release of all hostages and an end to the Hamas government in Gaza, a half-dozen Israeli officials and senior advisers told NBC News.