By Nidal al-Mughrabi and James Mackenzie

CAIRO/JERUSALEM (Reuters) - An Israeli-American hostage crossed into Israel on Monday after his release by Hamas as fighting paused in Gaza, the Israeli military said, but there was no deal on a wider truce or hostage release as monitors warned of famine in the devastated enclave.

Israel's military said it had received Alexander after the International Committee of the Red Cross said it had facilitated his safe transfer from 19 months of captivity to Israeli authorities.

Alexander was the last American held by Hamas and Israel's Channel 12 said his condition was "low" without citing a source.

Al Jazeera television showed a photograph of him standing next to masked fighters and a Red Cross official. Unlike in previous hostage releases, he was wearing civilian clothes.

Fighting halted at midday in Gaza after Israeli Prime Minister Benjamin Netanyahu said Israel would pause its operations to allow safe passage for the hostage release.

Hamas said it was freeing Alexander as a goodwill gesture to U.S. President Donald Trump, who is visiting the region this week.

"Edan Alexander, American hostage thought dead, to be released by Hamas. Great news!" Trump wrote in capital letters on his social media platform earlier in the day.

Netanyahu said Alexander's release came thanks to his country's military pressure in Gaza and political pressure exerted by Trump.

The Israeli leader said he spoke with Trump on Monday where the U.S. president expressed commitment to Israel, according to a statement by Netanyahu's office.

Netanyahu has said there will be no ceasefire and that plans to intensify military action in Gaza continue.

The release, after four-way talks between Hamas, the United States, Egypt and Qatar, could open the way to freeing the remaining 58 hostages held in the Gaza Strip, 19 months after Hamas' attack on Israel on October 7, 2023.

Qatar and Egypt said Alexander's release was an encouraging step towards new truce talks. Israel will send a delegation to Qatar on Thursday to discuss a new proposal aimed at securing further hostage releases, Netanyahu's office said.

Netanyahu has insisted that Israel's planning for an expanded military campaign in Gaza will continue, as one of his far-right coalition partners, national security minister Itamar Ben-Gvir, said the war on Islamist militant Hamas must not end and aid should not be let into the Palestinian enclave.

"Israel has not committed to a ceasefire of any kind," Netanyahu's office said, adding that military pressure had forced Hamas into the release.

Gaza health authorities said an Israeli strike killed at least 15 people sheltering at a school on Monday before fighting paused. Israel's military said it had targeted Hamas fighters there who were preparing an attack.

The global hunger monitor, the Integrated Food Security Phase Classification (IPC) reported on Monday that half a million people in the Gaza Strip face starvation and there is a critical risk of famine by September.

'BRING THEM ALL HOME'

Trump is due to visit Gulf states on a trip that does not include a stop in Israel but special envoy Steve Witkoff, who helped arrange the release, was expected in Israel on Monday, two Israeli officials said.

Alexander's family thanked Trump and Witkoff, saying in a statement that they hoped the decision would open the way for the release of the other remaining hostages.

"We urge the Israeli government and the negotiating teams: please don't stop," they said.

U.S. officials have tried to calm fears in Israel of a growing distance between Israel and Trump, who last week announced an end to U.S. bombing of Iran-backed Houthis in Yemen, who have continued to fire missiles at Israel.

Israel's government has drawn criticism over the deal to release Alexander, which laid bare the priority given to hostages able to rely on the support of a foreign government.

Einav Zangauker, whose son Matan is among 21 hostages still believed to be alive, said Netanyahu was choosing his political survival over ending the war.

Addressing Trump in a statement she read with other hostage families, she said: "The Israeli people are behind you. End this war. Bring them all home".

Netanyahu, who was due to testify in the latest session of his trial on corruption charges that he denies, has faced pressure from hardliners in his cabinet not to end the war.

Following a ceasefire agreement that halted fighting in Gaza for two months and allowed the exchange of 38 hostages for Palestinian prisoners and detainees in Israeli jails, Israel resumed its military campaign in the enclave in March.

Since then, it has extended its control of the territory, clearing around a third of what it has described as a "security zone" and blocked off the entry of aid into Gaza, leaving the 2 million population increasingly short of food.

Last week, U.S. Ambassador to Israel Mike Huckabee outlined plans for a new system of aid deliveries by private contractors, but many details are unclear, including on funding.

German President Frank-Walter Steinmeier told visiting Israeli President Isaac Herzog on Monday that humanitarian aid in Gaza needed to resume immediately. Herzog said the new aid mechanism would reach civilians, not Hamas, and urged the international community to help implement it.

Israeli forces invaded Gaza in retaliation for the Hamas-led assault on Israel in October 2023 that killed 1,200 people and saw 251 taken hostage, according to Israeli tallies.

Since then, more than 52,000 Palestinians have been killed, Palestinian health authorities say, and large swathes of the heavily built-up enclave have been laid to waste.

(Reporting by James Mackenzie, Maayan Lubell and Nidal al-Mughrabi; Additional reporting by Steve Holland and Rami Ayyub in Washington; Writing by James Mackenzie and Angus McDowall; Editing by Clarence Fernandez, Timothy Heritage, Ros Russell and Mark Heinrich)