Washington DC - President Joe Biden pushed Israeli Prime Minister Benjamin Netanyahu to quickly reach a Gaza ceasefire Thursday, with a friendly handshake masking tense ties and questions over the outgoing US leader's relevance.

The two leaders put on a good-humored show for the cameras as they met in the Oval Office at the White House, just four days after the 81-year-old Biden's stunning announcement that he would not seek reelection.

"From a proud Zionist Jew to a proud Zionist Irish American, I want to thank you for 50 years of public service and 50 years of support for the State of Israel," Netanyahu said in tribute to Biden at the start of the Oval Office meeting.

"And I look forward to discussing with you today and working with you in the months ahead."

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But Netanyahu (74) was also set to meet separately with Vice President and presumptive Democratic presidential nominee Kamala Harris – reflecting the new political reality of Biden being a lame duck for the next six months.

Harris has been more outspoken on Gaza in the past, and there has been speculation that she could adopt a tougher approach on Israel. Officials deny there is any "daylight" between her and Biden.

The White House said Biden would keep pushing for a ceasefire and hostage release deal between Israel and Hamas, a potentially legacy-defining achievement if it happens.

And it said it still believed that Netanyahu was ready for an agreement despite a fiery speech to the US Congress on Wednesday in which he vowed "total victory" against Hamas.

"The president will be reaffirming for prime minister Netanyahu that he believes we need to get there, and we need to get there soon," National Security Council spokesman John Kirby told reporters.

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"We can achieve a deal, but it's going to require, as it always does, some leadership, some compromise."

Biden and Netanyahu later met the families of US hostages held in Gaza, many of whom have called on Netanyahu to reach a deal.

Protesters chanted slogans outside a ring of metal barriers erected around the White House, following rowdy protests during Netanyahu's speech to lawmakers.

Harris on Thursday condemned the "despicable" and "unpatriotic" burning of an American flag by protesters after attempts by Donald Trump's Republicans to paint Democrats as pro-Hamas.

While Biden has continued to send billions of dollars' worth of deadly weapons to Israel since Hamas's October 7 attacks, relations with Netanyahu have been deeply strained by Israel's conduct during the war.

The meeting was the first time that Netanyahu had visited the White House during Biden's presidency. They also met in New York last year and when Biden traveled to Israel days after the attacks and hugged Netanyahu at the airport.

A senior US administration official said Wednesday that negotiations on a Gaza deal were in the "closing stages" and that Biden would try to close some "final gaps" with Netanyahu.

In a primetime speech on Wednesday explaining his decision to bow out of the election, Biden said he would "keep working to end the war on Gaza."

But in a further sign of Biden's diminishing relevance, and Netanyahu's determination to play both sides, the Israeli will meet Trump in Florida on Friday.

The ex-president on Thursday urged Israel to quickly "finish up" its war in Gaza, warning its global image was being tarnished.

Israel's assault on Gaza has left at least 39,000 dead – mostly civilians – though the true death toll is likely to be much higher.