The White House was careful not to get into specifics on the "extraordinarily generous" cease-fire proposal Secretary of State Antony Blinken spoke to earlier this morning, refusing to give specifics as they continued to call on Hamas to accept the proposal.

"I'm not going to characterize the proposal. I'm not going to get into any of the specifics. What we believe is that now is the time for Hamas to take this deal. It is on the table. It is time to, it is way past time to get these hostages home. It is way past time to get to a ceasefire and we need to make sure we continue to get that humanitarian aid," White House press secretary Karine Jean-Pierre said.

Jean-Pierre noted that Israel "has a lot on their plate," but expressed a desire for an in-person meeting to take place, in addition to the two virtual meetings the U.S. and Israel have had in recent weeks.

"We would like to have an in-person meeting. That is certainly what we would like to do, but in the meantime, we’ve had two important virtual meetings and in the readout, yesterday, we mentioned that the potential Rafah operations did come up between the two leaders in their conversation," she said.

Egyptian President Abdel Fattah El-Sisi also spoke to President Joe Biden Monday about ongoing Gaza talks and Egyptian efforts to reach a cease-fire and hostage deal in a phone call, the Egyptian presidency said in a statement.

The call discussed the risks of an Israeli incursion into Rafah, including the "catastrophic" impact on the worsening humanitarian crisis, and implications for the security and stability of the region, the statement added.

-ABC News' Molly Nagle and Ayat Al-Tawy

Israeli leaders are expressing concern over possible arrest warrants issued by the International Criminal Court against key officials, including Prime Minister Benjamin Netanyahu, an Israeli official, who spoke under condition of anonymity, told ABC News.

It is believed that such potential warrants might be related to charges on the scope of humanitarian aid Israel allowed into Gaza, according to the official.

The ICC can charge individuals with war crimes, crimes against humanity and genocide under its powers.

-ABC News' Dana Savir

At least 21 people were killed in Gaza after an Israeli airstrike Monday, the Al Kuwaiti Hospital in Rafah told ABC News. Six people were injured from the strike, the hospital added.

The updated death toll in Gaza is 34,488 killed and 77,643 injured, according to the Hamas-run Gaza Ministry of Health.

ABC News has reached out to the Israeli army for comment on the strike.

-ABC News' Dia Ostaz

U.S. Secretary of Antony Blinken, who is currently in Saudi Arabia, notably called for a cease-fire as "the most effective way to address the humanitarian crisis in Gaza" during a session with his counterparts of the Gulf Cooperation Council.

"The most effective way to address the humanitarian crisis in Gaza to alleviate the suffering of children, women and men and to create space for a more just and durable solution is to get a cease-fire and hostages home, but also not waiting on a cease-fire to take the necessary steps to meet the needs of civilians of Gaza," Blinken said.

"President Biden is insistent that Israel take specific concrete measurable steps to better address humanitarian suffering, civilian harm and the safety of aid workers in Gaza, including in his most recent call with Prime Minister Netanyahu," he added, referring to a Sunday call with the Israeli leader.

Blinken said the U.S. was "focused on addressing the greatest threat to regional stability and regional security -- Iran."

-ABC News' Lauren Minore

An Israeli official responded to the Biden administration's opposition to a military ground operation in Rafah saying, "we don't see eye to eye on everything, but we have been able to overcome differences".

The official added that, "Israel is a sovereign country that acts in accordance with its critical national interest."

-ABC News' Tom Soufi Burridge