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Israel's military said he was back inside Israel to be "reunited with his family".

Flag-waving crowds gathered to greet the convoy carrying Alexander, and in Tenafly, New Jersey, where he grew up, large crowds celebrated his release.

Close friends and family chanted his name and applauded at the news that Alexander had been freed, footage released by the Hostages and Missing Families Forum showed.

Israeli Prime Minister Benjamin Netanyahu hailed Alexander's return, adding: "The Government of Israel is committed to the return of all hostages and missing persons — both the living and the fallen."

He credited "political pressure" from Trump and "our military pressure" for the release.

The Forum in a statement urged Netanyahu to say he was "ready to negotiate a comprehensive agreement" to bring home all the hostages.

Meirav Etrogbar, 52, a volunteer at the Forum, told AFP: "They should stop the war and bring all the hostages back home in a deal, not military pressure."

Alexander's release comes a day after Hamas revealed it was engaged in direct talks with Washington towards a Gaza ceasefire.

"We affirm that serious and responsible negotiations yield results in the release of prisoners, while the continuation of aggression prolongs their suffering and may kill them," a Hamas statement said.

"We urge President Trump's administration to continue its efforts to end this brutal war." 

Alexander was the last living hostage in Gaza with American citizenship. His release came with Trump heading for Saudi Arabia on the first leg of a regional tour.

On Monday, Netanyahu thanked Trump "for his assistance in the release", and also said he had instructed a negotiating team to head to Qatar on Tuesday to discuss the further release of hostages.

Netanyahu earlier said "Israel has not committed to a ceasefire of any kind or the release of terrorists but only to a safe corridor that will allow for the release of Edan".

Negotiations for a possible deal to secure the release of all hostages would continue "under fire, during preparations for an intensification of the fighting", he added.

Meanwhile, the UN- and NGO-backed Integrated Food Security Phase Classification (IPC) warned Monday that Gaza was at "critical risk of famine", with 22 percent of the population facing an imminent humanitarian "catastrophe" after more than two months of a total aid blockade by Israel.

- 'Opportunity to breathe' -

Ahead of Alexander's release, a Hamas source said that mediators informed the group that Israel would halt military operations for the handover of the 21-year-old soldier.

The pause offered a much-needed respite for residents of the war-battered territory.

Somaya Abu Al-Kas, 34, who had been displaced to the southern city of Khan Yunis, said that "calm settled over Gaza, there was no shelling, and no nearby aircraft, which is very rare".

But Um Mohammed Zomlot, 50, also displaced in Khan Yunis, said: "Everyone is afraid that the shelling might resume suddenly after the prisoner is released."

Gaza's civil defence agency earlier reported at least 10 killed in an overnight Israeli strike on a school housing displaced people.

- 'Good faith gesture' -

After Hamas announced Sunday it would release Alexander, Trump hailed the "monumental news" in a post on social media, describing it as a "good faith gesture".

"Hopefully this is the first of those final steps necessary to end this brutal conflict," he added.

Egypt and Qatar, which along with the United States have mediated talks between Hamas and Israel, called it "an encouraging step toward a return to the negotiating table" in a joint statement.

Of the 251 hostages seized during Hamas's October 7, 2023 attack on Israel, 57 are still held in Gaza, including 34 the Israeli military says are dead.

Israel ended a two-month ceasefire on March 18, ramping up its bombardment of the territory.

Earlier this month, Israel's government approved plans to expand its Gaza offensive, with officials talking of retaining a long-term presence there.

Hamas's 2023 attack on southern Israel resulted in the deaths of 1,218 people, mostly civilians, according to an AFP tally based on official figures.

The health ministry in Hamas-run Gaza said Monday at least 2,749 people have been killed since Israel resumed its campaign, bringing the overall death toll since the war broke out to 52,862.

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