Washington (AFP) - Saudi Arabia's crown prince Mohammed bin Salman rounded off a weeks-long tour of the United States with a weekend in Texas, where he met Saturday with both former president Bushes.

George H.W. Bush, 93, tweeted a photo of the prince with his son, George W. Bush.

"A wonderful chance to celebrate the long-standing friendship between our two nations.", George Bush Senior wrote, while the Saudi embassy in Washington described the meeting as a "reminder of the strength and breadth of the long-standing Saudi-U.S. partnership."

The prince -- or MBS, as he is known -- traveled with his plentiful entourage from the White House to Houston via Boston, New York, Seattle, Los Angeles and Silicon Valley, embarking on what one expert called a particularly well-planned public relations campaign.

The Saudi regime faced little criticism along the way -- although Los Angeles Mayor Eric Garcetti expressed "concerns about human rights and the ongoing humanitarian crisis in Yemen," his office told AFP.

But strengthening US-Saudi relations in the face of Iran was a priority for US President Donald Trump, who hailed the nations' "great friendship" as he met with the 32-year-old prince at the Oval Office on March 20.

Since that meeting, MBS has been diligently pushing his "Saudi Vision 2030" -- a plan for a Saudi economy less reliant on oil and eager to attract US investors tempted by potential diversification.

The latter part of his trip saw him meet with directors of Google, Facebook and Palantir -- not to mention Microsoft founder-turned-philanthropist Bill Gates and Richard Branson, with whom he talked space exploration.

The prince also enjoyed a Hollywood dinner with Rupert Murdoch, where they were joined by studio bosses and actors including Morgan Freeman, according to the Hollywood Reporter. The meeting came ahead of the opening of Saudi Arabia's first cinema -- managed by American AMC Entertainment -- in Riyadh on April 18.

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Then, it was off to Houston to meet with the Bushes, having already met with Bill Clinton in New York. In fact, in terms of former presidents, only Barack Obama -- whose terms in office marked strained relations with Saudi Arabia -- was left off the agenda.

- Economic pay off? -

Prince Mohammed is scheduled to arrive in Paris on Sunday for an official visit on Monday and Tuesday -- including dinner with President Emmanuel Macron Tuesday evening. He set off on his international charm offensive in Egypt on March 4, before making his way to Britain and the US. After France, his next stop is Spain.

"In public relations for him it was incredibly successful," Simon Henderson, an expert on Saudi Arabia at the Washington Institute, told AFP of the US trip.

A browse of the prince's Instagram account reveals dozens of photos of him, all smiles and often dressed down without a tie, accompanied by various business leaders.

He has overcome a challenge for a Saudi royal: to appear "an ordinary sort of person (...) by turning up in Starbucks for instance," Henderson added, referencing the prince's coffee run with former New York mayor Michael Bloomberg.

"The question which I'm fascinated by is: he clearly got the PR he wanted to here, and it played well here. But how did it play at home?" Henderson said.

But while it seemed a fruitful tour in terms of diplomacy, it has yet to be seen if it will pay off economically.

Indeed, it's not clear whether Prince Mohammed's pitch to invest in Saudi Arabia would convince US business leaders while his anti-corruption campaign targeted hundreds of princes, ministers and businessmen -- a climate which makes identifying sustainable partners a tough task for Americans, according to Henderson.