Israel-Gaza live updates: Hamas publishes names of 20 living Israeli hostages to be released

Asked if he expects a Gaza or hostage deal on Tuesday, which will mark two years since Hamas' Oct. 7 attack on Israel, President Donald Trump said, "I think we’re going to have it soon."

"It's a hard thing for me to say that when for years and years, they’ve been trying to have a deal with Gaza," Trump said while taking questions in the Oval Office on Monday. "But we're going to have a Gaza deal, I'm pretty sure, yeah."

He cited the support of countries including Turkey and Saudi Arabia in trying to reach a peace deal.

"Everybody is on our side to get this deal done," he said.

White House press secretary Karoline Leavitt said the administration is "working very hard to move the ball forward as quickly as we can" as the ceasefire talks are underway.

"Technical talks" are ongoing and joined by Special Envoy Steve Witkoff and Jared Kushner, she said during a press briefing Monday afternoon.

"[President Donald Trump] wants to see a ceasefire. He wants to see the hostages released, and the technical teams are discussing that as we speak, to ensure that the environment is perfect to release those hostages," Leavitt said. "They're going over the lists of both the Israeli hostages and also the political prisoners who will be released."

Leavitt did not address how long the White House expects technical talks to last or if Trump is providing Hamas a new timeline to reach an agreement on his peace plan.

The first round of indirect negotiations between Israel and Hamas are underway in Sharm el-Sheikh, according to two sources familiar with the talks.

-ABC News' Jordana Miller

An average of 92 Palestinians have been killed each day in Israel Defense Forces attacks on the Gaza Strip across the 730 days since Oct. 7, 2023, according to a Monday statement from the Government Media Office in the Hamas-run territory.

Tuesday will mark the two-year anniversary of Hamas' Oct. 7 attack into Israel, which sparked the current conflict. Since then, a total of 67,139 Palestinians have been recorded as killed by IDF attacks, according to Hamas-run Gaza Health Ministry data published Sunday.

The media office said that an average of 27 children have been killed each day over the past two years, meaning more than one child per hour, every day for two years.

The media office did not specify how many of the Palestinians killed since October 2023 were militants.

-ABC News' Samy Zyara and Somayeh Malekian