WASHINGTON (BLOOMBERG) - In the balmy backyard of the Israeli President's residence last week, US President Joe Biden was reminded of "a great enthusiasm" for the Jewish state when he first came as a senator 50 years ago.

The next day, at his first meeting with Saudi Crown Prince Mohammed bin Salman, no one would believe Mr Biden was enthusiastic.

The awkward encounter - embodied by a grudging fist bump with a leader he had hoped to marginalise after the killing of columnist Jamal Khashoggi - underscored his calculus as a President desperate to bring home relief from high gasoline prices.

For the Crown Prince, the meeting delivered the stamp of United States legitimacy.

His officials worked to seize the opportunity to dispense with blame for Khashoggi's murder and convey the notion that Saudi Arabia holds the key to lower fuel prices.

Mr Biden and the Crown Prince pushed through a tightly choreographed summit designed to repair ties while avoiding the suggestion that Mr Biden was too chummy or obsequious.

The goal was clear: The US was turning the page and avoiding anything that would endanger more oil production.

It was a gamble by Mr Biden, who returns to Washington in precarious political standing.

His legislative agenda is mired down by his own party, with midterm elections just months away and allies increasingly frustrated that his White House has not achieved many of its aims.

The Saudi wager prompted howls of hypocrisy from activists and allies at home and in the Gulf states whom Mr Biden needs to address energy shortages.

The payoff may be months away - if it comes at all.

Mr Biden departed Saudi Arabia on Saturday without a firm commitment for a production hike that could ease pain at the pump, saying only that based on his conversations, he expects "further steps in the coming weeks".

That suggests an announcement may be delayed until the August meeting of the Organisation of the Petroleum Exporting Countries (Opec), that increases will not be calibrated until early fall and any drop in US gasoline prices will fall close to the November elections.

Even then, it is unclear if Gulf countries plan to boost production, a potentially crucial distinction given the looming end of US strategic-reserve sales and coming European sanctions on Russian energy.

Highlighting the limits of the President's control, crude prices have declined about 17 per cent since Mr Biden announced his Saudi visit in June, as recession fears overtook supply concerns.

According to Bloomberg Economics models, the chances of a downturn by the start of 2024 were close to 75 per cent as at last month.

Mr Biden's whirlwind tour of Tel Aviv, Jerusalem, Ramallah, Bethlehem and Jeddah - meeting along the way with the leaders of Israel, the Palestinian Authority, Gulf states, Egypt, Jordan and Iraq - offered few other near-term foreign policy victories.

The President brokered a historic agreement between the Israelis and Saudi Arabia, which opened its airspace in a decision that should reduce flight times between Israel and Asia.

US peacekeeping troops will depart a pair of islands in the Red Sea, paving the way for Saudi Arabia to take control and develop it.

Mr Biden and his aides insisted that the agreements represented the first step in what would be a signature accomplishment - normalising relations between Israel and Saudi Arabia.

"This is a big deal," Mr Biden told reporters on Saturday.

"This is the first tangible step in the path of what I hope will eventually be a broader normalisation of relations."

US hopes for a regional air defence shield in which Israel and Gulf nations would share defence technologies and intelligence to protect themselves from Iran and its proxies went unrealised.

Many in the region were focused - like Americans - on the optics of Mr Biden's visit with the Saudi leader known as MBS.

US officials attempted to limit the fallout from the meeting, US officials had told the Saudis to dispense with fanfare like the elaborate airport greetings, sword-dancing displays and glowing orbs that greeted former president Donald Trump on his trip to the kingdom. Mr Biden's fist bump with MBS, a gesture the White House attributed to coronavirus concerns, avoided a traditional greeting.

Mr Biden also made a point to raise the Khashoggi killing and his belief in the Crown Prince's culpability at the top of their meeting.

The Saudis countered by releasing images of Mr Biden and Prince Mohammed smiling and talking, showing the futility of any US attempts to deny his legitimacy.

Returning to the White House on Saturday just before midnight, Mr Biden brushed off a reporter who asked whether he regretted the fist bump.

"I'm happy to answer questions that matter," he said.