WASHINGTON/JERUSALEM (Reuters) - U.S. President Joe Biden on Friday laid out what he described as a three-phase Israeli proposal for a ceasefire in Gaza in return for the release of Israeli hostages, saying "it's time for this war to end" and winning a positive initial reaction from Hamas.

The first phase involves a six-week ceasefire when Israeli forces would withdraw from "all populated areas" of Gaza, some hostages - including the elderly and women - would be freed in exchange for hundreds of Palestinian prisoners, Palestinian civilians would return and 600 trucks a day would bring humanitarian aid into the devastated enclave.

In the second phase, of indeterminate length, Hamas and Israel would negotiate terms of a permanent end to hostilities, with the ceasefire extending as long as talks continue. The third phase would include a major reconstruction plan for Gaza.

"It's time for this war to end and for the day after to begin," said Biden, who is under election-year pressure to stop the Gaza conflict, now in its eighth month.

Hamas released a statement reacting positively to Biden's proposal, saying it was ready to engage "positively and in a constructive manner" with any proposal based on a permanent ceasefire, withdrawal of Israeli forces, the reconstruction of Gaza, a return of those displaced, and a "genuine" prisoner swap deal if Israel "clearly announces commitment to such deal".

Israeli Prime Minister Benjamin Netanyahu's office said he had authorized his negotiating team to present the deal, "while insisting that the war will not end until all of its goals are achieved, including the return of all our hostages and the destruction of Hamas' military and governmental capabilities."

Separately, the Israeli military said its forces have ended operations in north Gaza's Jabalia area after days of intense fighting, while probing further into Rafah in south Gaza to target what they say is the last major Hamas redoubt.

The conflict began on Oct. 7 when gunmen led by the Islamist Palestinian group stormed into southern Israel on motorcycles, paragliders and four-wheel drive vehicles, killing 1200 people and abducting more than 250 according to Israeli tallies.

Israel then invaded the Gaza Strip in what Netanyahu has called an effort to destroy Hamas, the militant Palestinian group that seized control of the area from the Fatah Palestinian faction in a violent struggle in 2007.

Talks mediated by Egypt, Qatar and others to arrange a ceasefire between Israel and Hamas have repeatedly stalled, with each side blaming the other for the lack of progress.

AN INDEFINITE WAR

In his speech, Biden called on the Israeli leadership to resist pressure from those in Israel who were pushing for the war to go on "indefinitely."

"There are those in Israel who will not agree with this plan. And will call for the war to continue indefinitely. Some are even in the government coalition," he said.

"They want to occupy Gaza. They want to keep fighting for years and hostages are not a priority for them. Well, I've urged leadership in Israel to stand behind this deal, despite whatever pressure comes," he added.

He implored Israelis not to miss the chance for a ceasefire.

"As the only American president who has ever gone to Israel at a time of war, as someone who just sent the U.S. forces to directly defend Israel when it was attacked by Iran, I ask you to take a step back, think what will happen if this moment is lost," he said. "We can't lose this moment."

The Gaza war has put Biden in a political bind.

On the one hand, he has long been a staunch supporter of Israel and would like to ensure funding and support from the pro-Israel community in the United States in his Nov. 5 election rematch against Republican former President Donald Trump.

On the other, progressive elements of Biden's Democratic party have grown increasingly angry at the president for the suffering the conflict has caused civilians in Gaza.

Palestinian health authorities estimate more than 36,280 people have been killed in Gaza since Israel attacked, and the United Nations says over a million people face "catastrophic" levels of hunger as famine takes hold in parts of the enclave.

In a sign of support for Israel despite the partisan divide in the United States, leaders of the Democratic-led U.S. Senate and of the Republican-led House of Representatives on Friday invited Netanyahu to address a joint meeting of Congress.

Several Israeli media outlets described Biden's speech on Friday as dramatic and interpreted it as an attempt to appeal directly to the Israeli public.

The week has been dominated by the fallout from an Israeli air strike in Rafah on Sunday that killed 45 Palestinians.

"The Palestinian people have endured sheer hell in this war," Biden said on Friday. "We all saw the terrible images from the deadly fire in Rafah earlier this week."

(Reporting by Steve Holland and Stephanie Kelly in Washington, James Mackenzie in Jerusalem; Additional reporting by Henriette Chacar, Nidal Al Mughrabi, Ahmed Tolba, Dan Williams and Patricia Zengerle; Writing By Arshad Mohammed, editing by Deepa Babington)

By Steve Holland and James Mackenzie