DOHA/TEL AVIV, Feb 8 (Reuters) - Mediators from the U.S., Qatar and Egypt scrambled to forge a ceasefire between Israel and Hamas in their four-month-old war in the Gaza Strip after America's top diplomat on a Middle East mission said there was still hope for a deal.

U.S. Secretary of State Antony Blinken said he saw room for negotiation, and a Palestinian Hamas delegation led by senior official Khalil Al-Hayya was due to travel on Thursday to Cairo for ceasefire talks with Egypt and Qatar.

Israeli Prime Minister Benjamin Netanyahu on Wednesday rejected Hamas' latest offer, calling it "delusional," and Hamas urged Palestinian armed factions to go on fighting.

"There are clearly nonstarters in what (Hamas has) put forward," Blinken said on Wednesday at a late-night press conference in a Tel Aviv hotel, without specifying what the nonstarters 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."

Before heading back to the U.S., Blinken was due to hold meetings in Israel on Thursday, including with family members of hostages still held in Gaza who have clamoured for Netanyahu to make winning their freedom his top priority.

Hamas, the militant group that rules Gaza, proposed a ceasefire 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 have told NBC News.

In response to the Hamas plan, Netanyahu renewed a pledge to destroy the Islamist movement, saying there was no alternative for Israel but to bring about its collapse.

"Surrendering to the delusional demands of Hamas ... will not only not bring the release of the hostages, it will invite another massacre. It will invite a grave disaster for the state of Israel that none of our citizens is willing to accept," the Israeli leader told reporters on Wednesday.

"Continued military pressure is a necessary condition for the release of the hostages," Netanyahu said.

Photo from Reuters