For many across the Middle East, the Israel-Hezbollah ceasefire came as a relief: the first major sign of progress in the region since war began more than a year ago.

But for Palestinians in Gaza and families of hostages held in the territory, the news appeared only to inaugurate a newer, grimmer period of the conflict there. For them, it marked yet another missed opportunity to end fighting that has stretched on for nearly 14 months.

U.S. President Joe Biden will launch a renewed drive Wednesday for a Gaza ceasefire and hostage release deal, now that Israel and Hezbollah have agreed to a truce in Lebanon, his national security adviser said.

The truce that began before dawn Wednesday in the south Lebanon war means Iran-backed Hezbollah is no longer fighting in solidarity with Hamas in Gaza. That will increase pressure on the militant Palestinian group to agree to a ceasefire and hostage deal, Jake Suillivan told MSNBC.

As a ceasefire between Israel and Hezbollah appears to hold in Lebanon, fighting raged on in the Gaza Strip on Wednesday.

The Gaza Health Ministry said 33 bodies had been brought to hospitals over the past 24 hours, raising the death toll in the nearly 14-month-long war to 44,282.

Hamas said it’s ready to cooperate with any effort to bring about a ceasefire in the Gaza Strip, after Israel and Hezbollah reached a truce to end months of fighting.

The deal does not address the war in Gaza. International mediators have repeatedly failed to bring Israel and Hamas to a deal that would end the brutal, 13-month-long war.

Israel's "ultimate goal" is to bring home hostages held by Palestinian militant group Hamas in Gaza, Defense Minister Israel Katz said Wednesday after the start of a ceasefire in Lebanon.

"We intend to make every effort to create the conditions for a new hostage exchange and bring everyone home –- this is the most important moral goal we face now, this is the ultimate goal," Katz said.

Provisions for immunity from prosecution at the International Criminal Court apply to Israeli Prime Minister Benjamin Netanyahu, the French foreign ministry said Wednesday.

In a statement, the ministry reaffirmed its commitment to international justice after the ICC issued an arrest warrant for Netanyahu, but also said that the Israeli leader was covered by immunity rules that apply to states which are not a party to the ICC. Israeli is not an ICC member.

Israel conducted strikes on the Syrian border with Lebanon that a war monitor said killed seven people, hours ahead of a Hezbollah-Israel ceasefire.

Syria’s defense ministry said six people were killed in Israeli strikes on border crossings with Lebanon just after midnight on Wednesday.

One of the most powerful Iran-backed factions in Iraq said it would continue its operations in support of Gaza despite the Israel-Hezbollah ceasefire.

Iraqi militias have repeatedly launched attacks on Israel from Iraq in the nearly 14 months since the Israel-Hamas war broke out.

The independent civilian commission of inquiry into the October 2023 Hamas attack on Israel has found Prime Minister Benjamin Netanyahu directly responsible for the failures leading up to the attack, alongside former defense ministers, the army chief and the heads of the security services.

The civil commission presented its findings today after a four-month probe in which it heard some 120 witnesses. It was set up by relatives of victims of the Hamas attack, in response to the absence of any state probe.

The U.N. rights chief is gravely concerned over the escalating conflict between Israel and Hezbollah in Lebanon and wants a "permanent ceasefire" there and in war-ravaged Gaza, his spokesman said Tuesday.

"The only way to end the suffering of people on all sides is a permanent and immediate ceasefire on all fronts: in Lebanon, in Israel and in Gaza," Jeremy Laurence, a spokesman for Volker Turk, told reporters in Geneva.