Israel-Gaza updates: Harris to meet with Israeli war Cabinet member on Monday

After President Joe Biden said Monday he "hopes" to see a cease-fire reached by March 4, State Department spokesperson Matthew Miller said Tuesday that Biden’s optimism stemmed from "the broad outlines of a deal" agreed to by Israel, the U.S. and other partners last week, as well as “negotiations that are continuing through this week.”

But Miller said Hamas wields significant control over when and whether a deal is reached.

"Certainly, we'd welcome getting one by this weekend," Miller said. "What I can say about the overall progress is that we made significant progress towards an agreement last week when we had officials from United States government engaging in the region. We continue to pursue further progress this week."

"We are trying to push this deal over the finish line -- we do think it's possible," Miller said.

-ABC News’ Shannon Crawford

A senior Israeli political source told ABC News on Tuesday that Israeli Prime Minister Benjamin Netanyahu was "surprised" by President Joe Biden's remarks that he was hopeful a cease-fire between Israel and Hamas could be in place "by next Monday."

Netanyahu said in a statement later on Tuesday, "Since the beginning of the war, I have been leading a political campaign whose purpose is to curb the pressures intended to end the war before its time, and on the other hand also to gain support for Israel."

"We have significant successes in this area, because today the Harvard-Harris survey is published in the United States, which shows that 82% of the American public supports Israel," he continued. "This gives us two more strength to continue the campaign until the complete victory."

-ABC News' Zoe Magee, Jordana Miller and Morgan Winsor

An Israeli official told ABC News on Tuesday that the United Nations Relief and Works Agency for Palestine Refugees in the Near East (UNRWA) is "intertwined with terror and needs to be dissolved."

"Their sole goal was to perpetuate the Palestinian refugee problem," the official said. "Their compliance with Hamas terrorism and incitement was exposed. Any prospect for peace depends on dissolving UNRWA."

The Israeli official said humanitarian aid in the war-torn Gaza Strip should be provided by people "who are not associated with Hamas or UNRWA."

ABC News has reached out to UNRWA for comment.

In a dossier released in late January, the Israeli military alleged that 13 UNRWA employees participated in the Hamas-led Oct. 7 terror attack on Israel.

UNRWA has said it is investigating the allegations and took swift action against those accused of being involved in the attack. However, the United States and other top donors have suspended their funding to the agency, which is the biggest humanitarian aid provider in Gaza.

-ABC News' Jordana Miller and Morgan Winsor

A spokesperson for the Qatari Ministry of Foreign Affairs said Tuesday that there is no breakthrough to announce concerning a potential deal between Israel and Hamas on a cease-fire and hostage release.

"Many developments have occurred. Nothing to announce today, but we feel optimistic," the spokesperson told reporters.

The spokesperson said the talks remain "ongoing" and they cannot comment on U.S. President Joe Biden's remarks that a deal is expected by next Monday.

Qatar, along with Egypt and the United States, has been mediating talks between the warring sides.

-ABC News' Emma Ogao and Morgan Winsor