Israel-Gaza-Lebanon updates: Officials say 87 killed in Israeli strikes on Beit Lahia

U.S. officials sent a letter to Israeli officials demanding that Israel take steps within 30 days to improve the humanitarian situation in Gaza, or Israel will face consequences with a potential change in U.S. policy, two Israeli sources confirmed to ABC News.

U.S. Secretary of State Antony Blinken and Secretary of Defense Lloyd Austin sent a letter to Israeli Minister of Strategic Affairs Ron Dermer and Israeli Minister of Defense Yoav Gallant Monday focusing on increasing the supply of humanitarian aid into Gaza by the beginning of winter, facilitating the aid delivery route through Jordan and ending the "isolation" of northern Gaza.

"Failure to demonstrate a sustained commitment to implementing and maintaining these measures may have implications for US policy under NSM-20 and relevant US law," the letter stated.

The National Security Memorandum, or NSM-20, states the secretaries of State and Defense are "responsible for ensuring that all transfers of defense articles and defense services" by the departments under "any security cooperation or security assistance authorities are conducted in a manner consistent with all applicable international and domestic law and policy, including international humanitarian law and international human rights law," according to the law.

Deputy Pentagon press secretary Sabrina Singh confirmed Austin and Blinken sent a letter to their Israeli counterparts over humanitarian conditions in Gaza, but refused to give additional details.

"I can confirm that Secretary Austin with Secretary Blinken, they co-signed a letter that went to their Israeli counterparts. This was personal, private correspondence, so I'm not going to get into more specifics of it, other than it was expressing concern about the humanitarian conditions in Gaza," Singh said on Tuesday.

The letter was first reported by Israeli media and Axios reporter Barak Ravid.

-ABC News' Jordana Miller, Dorit Long and Matt Seyler

Over 25% of Lebanon is now under Israeli evacuation orders as Israeli airstrikes continue to increase the number of areas impacted, according to the United Nations refugee agency.

"We have over 25% of the country under a direct Israeli military evacuation order. Just yesterday, we had another 20 villages issued with an evacuation order in the south of the country," Rema Imseis, U.N. High Commissioner for Refugees director for the Middle East, said Tuesday.

"In a country of that size, which is relatively small, and a population that's estimated around 5 million people, you can imagine how dramatic it is that over 1 million people are now without shelter and on the move ... being forced to flee their homes in search of safety," Imseis said.

-ABC News' Guy Davies

Hezbollah Deputy Secretary-General Sheikh Naim Qassem said it is "impossible to separate Lebanon's front from Palestine," in a recorded video address released on Tuesday.

There had been speculation over whether Hezbollah would be open to a cease-fire agreement that didn't include Gaza.

Israeli officials have asserted that the aim in Lebanon is to return Israelis home to the north and separate the war in the north from the war in Gaza.

-ABC News' Guy Davies

Pentagon Press Secretary Maj. Gen. Pat Ryder said in a statement Tuesday that American troops are already in Israel to support the deployment of a Terminal High-Altitude Area Defense (THAAD) battery to the country.

"An advance team of U.S. military personnel and initial components" required to operate the system arrived in Israel on Monday, Ryder said.

"Over the coming days, additional U.S. military personnel and THAAD battery components will continue to arrive in Israel," he added.

"The battery will be fully operational capable in the near future, but for operations security reasons we will not discuss timelines," Ryder said.

-ABC News' Luis Martinez