Israel-Gaza-Lebanon live updates: American hostage's father makes plea to Biden and Trump

A cease-fire deal between Israel and Hezbollah is close, White House National Security spokesperson John Kirby reiterated in a briefing Tuesday, but he would not give details about the deal or specific timing, saying he had to be careful not to get in the way of the tenuous diplomacy.

"We believe that the trajectory of this is going in a very positive direction. But again, nothing is done until everything is done. Nothing's all negotiated till everything is negotiated. And you know, we need to keep at the work to see it through so that we can actually get the ceasefire for which we've been working for for so long and so hard," Kirby said.

Kirby declined to say if any announcement from President Joe Biden and French President Emanuel Macron should be expected over the next few days.

-ABC News' Cheyenne Haslett

Israel's far-right National Security Minister Itamar Ben-Gvir said Monday that a potential cease-fire agreement to end the fighting in Lebanon would be "a big mistake."

Ending the war would be a "missed opportunity" to "eradicate Hezbollah," Ben-Gvir wrote on X.

Ben-Gvir has previously pressured Prime Minister Benjamin Netanyahu to reject any cease-fire deal in Gaza, where fighting continues with Hamas and other militant groups.

"We must continue until the absolute victory," Ben-Gvir said of both the Gaza and Lebanon fronts.

-ABC News' Jordana Miller

In an address to thousands of Basij militia members on Monday, Iranian Supreme Leader Ayatollah Ali Khamenei said the International Criminal Court arrest warrants issued last week for Israeli Prime Minister Benjamin Netanyahu and former Defense Minister Yoav Gallant were insufficient.

"What [they have] done in Gaza and Lebanon is not a victory, it is a war crime," Khamenei said.

"Now they have issued arrest warrants for them; this is not enough," he added of the ICC decision. "A death sentence must be issued for Netanyahu and the criminal leaders of this regime."

The ICC also issued an arrest warrant for Hamas military commander Mohammed Deif, who the Israel Defense Forces claimed to have killed in an airstrike in Gaza in July.

Netanyahu's office expressed its "disgust" at the decision and dismissed the ICC warrant as "absurd."

-ABC News' Somayeh Malekian and Joe Simonetti

The Israel Defense Forces said its warplanes "conducted intelligence-based strikes on several Hezbollah command centers" in southern Beirut on Monday.

The strikes again focused on the Dahiya area in the south of the Lebanese capital, which is known as a Hezbollah stronghold.

Monday's bombings followed an intense day of strikes on Sunday, as diplomats continued to push for a cease-fire agreement to end the fighting between Israel and Hezbollah.

-ABC News' Jordana Miller and Joe Simonetti