Lucia Suarez Sang is an associate managing editor at CBSNews.com. Previously, Lucia was the director of digital content at FOX61 News in Connecticut and has previously written for outlets including FoxNews.com, Fox News Latino and the Rutland Herald.

President Trump urged negotiators set to meet Monday for crucial talks aimed at ending the war in Gaza to "move fast" as hopes for a peace deal grew after Prime Minister Benjamin Netanyahu said a hostage release could be announced this week.

Tuesday marks two years since the Hamas terrorist attack on Israel on Oct. 7, 2023, that sparked the war.

"There have been very positive discussions with Hamas, and Countries from all over the World (Arab, Muslim, and everyone else) this weekend, to release the Hostages, end the War in Gaza but, more importantly, finally have long sought PEACE in the Middle East," Mr. Trump wrote on Truth Social on Sunday. "These talks have been very successful, and proceeding rapidly."

He added: "The technical teams will again meet Monday, in Egypt, to work through and clarify the final details. I am told that the first phase should be completed this week, and I am asking everyone to MOVE FAST. I will continue to monitor this Centuries old 'conflict.' TIME IS OF THE ESSENCE OR, MASSIVE BLOODSHED WILL FOLLOW - SOMETHING THAT NOBODY WANTS TO SEE!"

On Friday, Hamas said it had accepted some elements from the U.S.-led peace plan that Mr. Trump outlined last month. Under the plan, Hamas would release the remaining 48 hostages -- about 20 believed to be alive -- within 72 hours. It would also give up power and disarm, which Hamas has not agreed to do.

The delegation led by top Israeli negotiator Ron Dermer will leave Monday for the talks in Sharm el-Sheikh, Netanyahu's office said. An Egyptian official said the Hamas delegation had arrived. U.S. special envoy to the Middle East, Steve Witkoff, and Jared Kushner, the president's son-in-law and senior adviser, are joining the talks, a senior U.S. official confirmed to CBS News.

Discussions will focus on the proposed exchange of hostages for Palestinian prisoners held by Israel, Egypt's foreign ministry said.

In a brief statement on Saturday, Netanyahu said he hopes to announce the release of all hostages "in the coming days" and that "our goal is to contain these negotiations to a time frame of a few days."

But he signaled there would not be a full Israeli withdrawal from Gaza, something Hamas has long demanded.

Secretary of State Marco Rubio told CBS News' "Face the Nation with Margaret Brennan" on Sunday that the release of hostages from Gaza is the "most emergent and immediate phase" of the peace plan.

"Beyond that is what happens after that, and that is, how do we ensure that we can create and help build a Gaza free of terrorism, free of Hamas, free of anything like Hamas," Rubio said. "And that's going to take work and some time not just to agree on, but to implement."

On the hostages, Rubio said the "expectation is that this happens quickly," though he wasn't clear on a specific deadline. He acknowledged that there are some logistical hurdles, including Israeli bombardment.

"Reality is, this is a war zone. I mean, this is a place that's suffered a tremendous amount of destruction. That fighting needs to stop," Rubio said. "You can't release hostages while there's still bombardments going on."

CBS News team members in East Jerusalem reported that there were Israeli bombardments underway, including strikes on Saturday.

As hundreds of thousands of people marched across Israel, several European cities and elsewhere in support of ending the war, the foreign ministers of eight Muslim-majority countries issued a joint statement welcoming steps toward a possible ceasefire.

They also underlined their commitment to the return of the Palestinian Authority to Gaza, unifying Gaza and the West Bank and reaching an agreement leading to a "full Israeli withdrawal" from Gaza.

Israel and Hamas have been at war since Oct. 7, 2023, when Hamas-led terrorists attacked southern Israel, killing some 1,200 people and taking 251 hostages. Since then, Israel has waged an intense aerial bombardment and ground campaign in the Gaza Strip. More than 66,000 Palestinians have been killed, according to the Hamas-run Gaza Health Ministry, which does not specify how many of the dead were civilians or militants.

Trump urges Gaza peace deal negotiators to "move fast" as meeting set to begin in Cairo