JERUSALEM/DOHA, Feb 2 (Reuters) - Israel prepared to advance its war on Gaza farther south, close to the Egyptian border, after claiming to have dismantled Hamas in Khan Younis, as diplomatic efforts in pursuit of a ceasefire accelerated.

Defence Minister Yoav Gallant said on Thursday that success in the fight against the Palestinian militants in the southern Gaza city of Khan Younis, where Israel launched a major ground attack last week, meant its forces could advance to Rafah on the enclave's southern border.

More than half of Gaza's 2.3 million people are sheltering in this area, mainly cold and hungry in makeshift tents and public buildings.

"We are achieving our missions in Khan Younis, and we will also reach Rafah and eliminate terror elements that threaten us," Gallant said in a statement.

At the same time, Qatari and Egyptian mediators hoped for a positive response from Hamas, which runs Gaza, to the first concrete proposal for an extended halt to fighting, agreed with Israel and the U.S. at talks in Paris last week.

A Palestinian official close to the negotiations told Reuters the text envisages a first phase of 40 days, during which fighting would cease while Hamas freed remaining civilians among the more than 100 hostages it still holds. Further phases would see the handover of Israeli soldiers and bodies of dead hostages.

Such a long pause would be a first since Oct. 7, when Hamas fighters attacked Israel, killing 1,200 people and capturing 253 hostages, precipitating an Israeli offensive that has laid waste to much of Gaza.

Health officials in the enclave said on Thursday the confirmed Palestinian death toll had risen above 27,000, with thousands more dead still lying under the rubble.