House Speaker Mike Johnson wrote a letter to President Biden on Wednesday urging the president to "leverage all American options and influence to support Israel in bringing these hostages home."

"I write today to express grave concern that your administration is not taking sufficient steps to ensure the release of American hostages who are detained by Hamas." Johnson said. "The United States must do everything in our power to support Israel’s right to self-defense, and work toward the immediate release of hostages, including the remaining American citizens."

Johnson requested a briefing before July 10 on "the specific ways in which your administration plans to address the increasingly dire situation."

-ABC News’ Lauren Peller

In the wake of Israeli Prime Minister Benjamin Netanyahu’s claims that the U.S. has slowed the flow of weapons, White House national security communications adviser John Kirby said that all the weapons continue to flow except "only one shipment of high-density, low-precision munitions that has been paused."

"Israel continues to get arms and ammunition," Kirby told reporters on Wednesday. "We want to make sure that they have what they need … that commitment will not waver."

Kirby did repeat the administration's message that they are "not going to respond" to all of Netanyahu’s public statements.

Israeli Minister of Defense Yoav Gallant said after his White House meeting with national security adviser Jake Sullivan, "We have made significant progress in addressing force buildup and munition supply."

Asked whether the U.S. would support Israel if the war escalated into a conflict on the northern border with Hezbollah, Kirby said more conflict with Hezbollah is not in Israeli's interest and reiterated America's support for Israel.

“We want to see no second front opened and we want to see if we can resolve the tensions up there through diplomatic processes,” Kirby said.

-ABC News’ Michelle Stoddart

Officials from the United Nations and the Israel Defense Ministry met to work on addressing security issues impacting aid distribution in Gaza, a U.S. official told ABC News.

-ABC News' Shannon Crawford

State Department spokesperson Matthew Miller on Tuesday addressed concerns that the United Nations could suspend humanitarian operations in Gaza as the conditions its workers face in the enclave have devolved from bad to worse.

"I can tell you this is an issue we have been intensely focused on," Miller said, adding that the State Department’s special envoy for Middle Eastern humanitarian issues has coordinated with the U.N. and Israeli entities to "try to figure out a way to allow U.N. workers to safely do their jobs."

Miller noted while some aid was flowing into Gaza through various points of entry and moving through the north, the U.S. had observed "over the past few weeks, a big backlog" at Kerem Shalom -- the border between Israel and southern Gaza -- due to a "breakdown in security on the ground." This was caused not by the Israel Defense Forces or Hamas, but by "random looting, and criminal gangs and criminal actors who are attacking trucks," Miller said.

Miller said U.N. aid workers will be provided with "personal protective equipment, radios and other communication devices so they can communicate with each other and safely move around Gaza."

Miller said, "Long term, we want to see a cease-fire and the reestablishment of Palestinian-led governance. And ultimately, we have ideas for providing security inside Gaza, providing governance and reconstruction -- all of these things that would go to a restoration of law and order. ... But that is a long term that in no way accounts for the here and now."

Miller also argued that the U.S. had a limited role it could play in increasing security for aid workers at this stage, saying it was ultimately an issue that Israel and the U.N. would have to address.

-ABC News’ Shannon Crawford

While addressing Israel's parliament on Monday, Israeli Prime Minister Benjamin Netanyahu said he remains "committed" to the Israeli hostage/cease-fire proposal that President Joe Biden had presented.

"Will not end the war until we return all the abductees -- 120 abductees -- both the living and the dead. We are committed to the Israeli proposal that President Biden welcomed. Our position has not changed," Netanyahu said.

He added, "We will not end the war until we eliminate Hamas and until we return the residents of the south and the north safely to their homes. … [And] we will thwart Iran's intentions to destroy us."

Senior Hamas official Khalil Al-Hayya told Al Jazeera on Monday evening that "Netanyahu's statements confirmed our view that he does not want a cease-fire or the return of [Israeli] prisoners. … Netanyahu's real stance is that he wants to retrieve his prisoners and continue the war."

"We are ready for genuine negotiations if Netanyahu adheres to the principles outlined by President Biden," he said. "We are ready for negotiations that achieve a cessation of aggression and a complete withdrawal from the Gaza Strip."

-ABC News’ Will Gretsky