Israeli Prime Minister Benjamin Netanyahu worked to mend ties with Republican presidential candidate Donald Trump on Friday and offered measured optimism about progress towards a ceasefire deal for Gaza.

At Mr Trump’s Florida Mar-a-Lago estate, where the two men met face-to-face for the first time in nearly four years, Mr Netanyahu told journalists he wanted to see US-mediated talks succeed for a ceasefire and release of hostages.

“I hope so,” Mr Netanyahu said when reporters asked if his US trip had made progress.

While Mr Netanyahu at home is increasingly accused of resisting a deal to end the nine-month-old war to stave off the potential collapse of his far-right government when it ends, he said Friday he was “certainly eager to have one. And we’re working on it”.

As president, Mr Trump went well beyond his predecessors in fulfilling Mr Netanyahu’s top wishes from the United States. Yet relations soured after Mr Netanyahu became one of the first world leaders to congratulate Joe Biden for his 2020 presidential victory, which Mr Trump continues to deny.

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Mr Netanyahu with Vice President Kamala Harris (Julia Nikhinson/AP)

The two men now have a strong interest in restoring their relationship, both for the political support their alliance brings and for the lustre it gives each with their conservative supporters.

A beaming Mr Trump was waiting for Mr Netanyahu on the stone steps outside his private club and residence in Palm Beach, Florida. He warmly clasped the hands of the Israeli leader.

“We’ve always had a great relationship,” Mr Trump insisted before journalists. Asked as the two sat down in a muraled room for talks if Mr Netanyahu’s trip to Mar-a-Lago was repairing their bond, Mr Trump responded: “It was never bad.”

For both men, Friday’s meeting was aimed at highlighting for their home audiences their depiction of themselves as strong leaders who have gotten big things done on the world stage, and can again.

Mr Netanyahu’s Florida trip followed a fiery address to a joint meeting of Congress on Wednesday that defended his government’s conduct of the war and condemned American protesters galvanised by the killing of more than 39,000 Palestinians in the conflict.

On Thursday, Mr Netanyahu met in Washington with Mr Biden and Vice President Kamala Harris, who appears on track to becoming the new Democratic presidential nominee after Mr Biden decided to step out of the race.

Both pressed the Israeli leader to work quickly to wrap up a deal to bring a ceasefire and release hostages held by Hamas.

Mr Trump’s campaign said he pledged in Friday’s meeting to “make every effort to bring peace to the Middle East” and combat antisemitism on college campuses if American voters elect him to the presidency in November.

Mr Netanyahu handed Mr Trump a framed photo that the Israeli leader said showed a child who has been held hostage by Hamas-led militants since the first hours of the war. “We’ll get it taken care of,” Mr Trump assured him.

In a speech later on Friday before a group of young Christian conservatives, Mr Trump said he also asked Mr Netanyahu during their meeting how “a Jewish person, or a person that loves Israel” can vote for Democrats.

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For Mr Netanyahu, repairing relations with Mr Trump is imperative (Alex Brandon/AP)

He also laced into Ms Harris for missing Mr Netanyahu’s speech and claimed she “doesn’t like Jewish people” and “doesn’t like Israel”.

Ms Harris has been married to a Jewish man for a decade.

For Mr Trump, the meeting was a chance to be cast as an ally and statesman, as well as to sharpen efforts by Republicans to portray themselves as the party most loyal to Israel.

Divisions among Americans over US support for Israel’s war against Hamas in Gaza have opened cracks in years of strong bipartisan backing for Israel, the biggest recipient of US aid.

For Mr Netanyahu, repairing relations with Mr Trump is imperative given the prospect that Mr Trump may once again become president of the United States, which is Israel’s vital arms supplier and protector.

One gamble for Mr Netanyahu is whether he could get more of the terms he wants in any deal on a Gaza ceasefire and hostage release and in his much-hoped-for closing of a normalisation deal with Saudi Arabia if he waits out the Biden administration in hopes that Mr Trump wins.

“Benjamin Netanyahu has spent much of his career in the last two decades in tethering himself to the Republican Party,” said Aaron David Miller, a former US diplomat for Arab-Israeli negotiations, now a senior fellow at the Carnegie Endowment for International Peace.

For the next six months, that means “mending ties with an irascible, angry president,” Mr Miller said, meaning Mr Trump.