Edan Alexander has been captive since Oct. 7.
A ceasefire went into effect at 4 a.m. local time Wednesday morning after Israel's Cabinet approved the U.S.-backed proposal to end the fighting between Israel and Hezbollah after prolonged negotiations.
The Israel Defense Forces continues its intense airstrike and ground campaigns in Gaza, particularly in the north of the devastated Palestinian territory.
Tensions also remain high between Israel and Iran after tit-for-tat long-range strikes in recent months and threats of further military action from both sides.
Israeli forces conducted strikes Monday in the southern suburbs of Lebanon's capital Beirut and in southern Lebanon as talks of a cease-fire between Hezbollah and Israel continued on both sides.
At least 31 people were killed and 62 others injured in the strikes on southern Lebanon, the Lebanese Ministry of Public Health said in a post on X.
-ABC News' Jordana Miller
There are no indications that Prime Minister Benjamin Netanyahu intends to call in his cabinet and vote to approve the Lebanon cease-fire Monday night, Israeli officials told ABC News.
Netanyahu is planning a series of meetings Tuesday to discuss the Lebanon cease-fire deal, including talks with his minister of strategic affairs, former American ambassador Ron Dermer, along with his most senior defense officials.
Later in the afternoon, Netanyahu will hold a larger cabinet meeting that includes the far-right. That meeting may lead to a final vote to approve a deal, though that remains unclear. A deal can pass even if one of the two far-right leaders opposes it.
The cease-fire would last for 60 days, but would not require the Israel Defense Forces to withdraw right away.
-ABC News' Joe Simonetti and Jordana Miller
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
