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.
President Joe Biden said Wednesday that the U.S. "will make another push with Turkey, Egypt, Qatar, Israel and others to achieve a ceasefire in Gaza" over the coming days, following the success of ceasefire talks in Lebanon.
Negotiations, Biden said in a post to X, must end "with the hostages released and an end to the war without Hamas in power."
-ABC News' Jordana Miller
Lebanon's caretaker Prime Minister Najib Mikati confirmed Lebanon's acceptance of the ceasefire in an address on Wednesday.
"We affirm the government's commitment to implementing Security Council Resolution 1701 in all its provisions," he said, referring to the 2006 U.N. Security Council measure that sought to end the last bout of cross-border fighting between Israel and Hezbollah.
Resolution 1701 stipulated that Hezbollah must withdraw all forces north of the Litani River and that all Israeli forces must leave -- and no longer violate the sovereignty of -- Lebanon.
Mikati did not address the separate U.S.-Israeli agreement backing Israel's right to continue to strike anywhere in Lebanon if deemed necessary for self-defense.
-ABC News' Ghazi Balkiz and Somayeh Malekian
Hezbollah allies on Wednesday praised the group for securing its ceasefire deal with Israel.
In a press conference Wednesday morning, Iranian Foreign Ministry spokesperson Esmaeil Baqaei said Tehran supports "ending Israel's aggression against Lebanon as a part of the ceasefire."
Iran -- the founder and director of the so-called "Axis of Resistance" of which Hezbollah is a key element -- maintains "unwavering support for the Lebanese government, people and resistance," Baqaei said.
Hamas, meanwhile, said in an official statement that it welcomed the ceasefire and praised Hezbollah's support of Palestinians, as well as the "great sacrifices" of the group's members including late leader Hassan Nasrallah.
Israel's acceptance of the deal, Hamas added, is a "milestone" in "destroying" Israeli Prime Minister Benjamin Netanyahu's "illusions of changing the map of the Middle East by force and his illusions of defeating or disarming the resistance forces."
Yemen's Houthis -- who have been attacking shipping and launching long-range strikes into Israel -- also praised Hezbollah's "steadfastness," framing the ceasefire deal as an Israeli defeat.
"The conflict with the Zionist enemy is an inevitable conflict and the wars with it are rounds in a conflict that will inevitably end with its demise," the Iran-backed group said in a statement.
-ABC News' Ghazi Balkiz, Samy Zyara and Somayeh Malekian
The Israel Defense Forces said its warplanes bombed "dozens" of Hezbollah targets across Lebanon in the hours leading up to the Wednesday morning ceasefire.
The IDF said in a post to social media that the targets included "Hezbollah command centers, launchers, weapons storage facilities and terrorist infrastructure sites in Beirut, Tyre and Nabatieh."
The IDF also struck "several smuggling routes between Syria and Lebanon, which were used by Hezbollah to smuggle weaponry," the force said.
-ABC News' Jordana Miller
