The Israel Defense Forces said on Tuesday that "operational plans for an offensive in Lebanon were approved and validated, and decisions were taken on the continuation of increasing the readiness of troops in the field."

White House officials are worried about a second war front opening between Israel and Lebanon at Israel’s northern border, dispatching a top aide to President Joe Biden to the region.

Amos Hochstein, a special envoy and deputy assistant at the White House, met Tuesday with Nabih Berri, the speaker of the Lebanese parliament.

"It's in everyone's interest to resolve it quickly and diplomatically. That is both achievable and it is urgent," Hochstein said, according to a transcript provided by the White House.

When asked if the two countries are on the brink of war, Hochstein said he believes a diplomatic solution is possible, adding, "But this is a very serious situation that we are in."

This meeting followed Hochstein’s in-person meetings with Israeli Prime Minister Benjamin Netanyahu and other Israeli officials on Monday.

White House national security spokesman John Kirby confirmed on Monday that the administration was concerned about the war in Gaza widening to Lebanon.

"If we weren't concerned about the possibility of escalation and a full blown, second front there, to the north, we wouldn't still be involved in such intense diplomacy that Mr. Hochstein is over there right now," Kirby told reporters in a press call.

-ABC News’ Anne Flaherty

Israeli Prime Minister Benjamin Netanyahu in a statement Tuesday criticized the U.S. for withholding certain weapons.

Netanyahu said when he met with Secretary of State Antony Blinken in Israel recently, he told Blinken, "It's inconceivable that in the past few months, the administration has been withholding weapons and ammunitions to Israel."

"Israel, America's closest ally, fighting for its life, fighting against Iran and our other common enemies," Netanyahu said. "Secretary Blinken assured me that the administration is working day and night to remove these bottlenecks. I certainly hope that's the case. It should be the case."

Netanyahu then quoted former U.K. Prime Minister Winston Churchill.

"During World War II, Churchill told the United States, 'Give us the tools, we'll do the job,'" Netanyahu said. "And I say, give us the tools and we'll finish the job a lot faster."

At a news conference Tuesday, Blinken declined to relate exactly what was said in private diplomatic conversations and did not deny that he had assured Netanyahu that the U.S. was working to remove bottlenecks inhibiting the supply of American arms and ammunition to Israel.

Blinken did repeatedly underscore the Biden administration’s commitment to Israel’s defense.

"It's very important to remember that our security relationship with Israel goes well beyond Gaza. Israel is facing a multiplicity of threats and challenges including in the north, from Hezbollah, from Iran, from the Houthis in the Red Sea, from various groups that are aligned against Israel and in many cases beholden to Iran," Blinken said.

President Joe Biden "will do everything he can to make sure that Israel has what it needs to effectively defend itself against these threats," Blinken said. "And a big part of that, as well, is making sure that in providing that assistance to Israel, it has a strong deterrent, which is the best way to avoid more conflict, to avoid more war, to avoid what we're already seeing in Gaza spreading to other areas."

White House press secretary Karine Jean-Pierre said the administration is surprised by Netanyahu’s claim of the U.S. withholding weapons.

“We generally do not know what he's talking about," she said Tuesday.

The Israeli military is "weeks" away from wrapping up the main part of its controversial ground invasion in and around Rafah in southern Gaza, Israel Defense Forces spokesperson Rear Adm. Daniel Hagari told ABC News.

"We are there to dismantle the military framework of the [Hamas'] Rafah Brigade," Hagari said on Monday.

"We are weeks now just from achieving this goal," he said.

The Israeli military now controls over 60% of the Rafah area, Israeli defense officials told ABC News on Monday.

-ABC News’ Tom Soufi Burridge, Hugo Leenhardt and Dana Savir

The Israel Defense Forces said Monday that its soldiers have killed Muhammad Mustafa Ayoub, describing him as a "key operative" in Hezbollah’s rocket and missile department in southern Lebanon.

Hezbollah confirmed Ayoub’s death in a brief statement.