Tehran (AFP) - The yawning gap between Tehran and Washington has grown even wider with US President Donald Trump's latest efforts to isolate Iran, which accused the United States of "milking" Saudi Arabia for petro-dollars.

Trump's choice of Saudi Arabia, Iran's bitter regional rival, for his first official foreign visit reflects the deep antagonism of his administration towards the Islamic republic.

The US president signed a giant list of deals, worth a total of $380 billion, including $110 billion for weapons that will invariably find their way into the numerous conflicts of the region -- including Syria, Yemen and Iraq -- where Riyadh and Tehran often find themselves on opposing sides.

Trump also vilified Iran as the greatest source of instability in the Middle East, though many observers noted the irony that his claims came on the same day that 41 million Iranians enthusiastically took part in elections, with a sizeable majority backing President Hassan Rouhani and his policy of engagement with the world.

Relations with the US and Iran have been under deep freeze since the Islamic revolution of 1979, which deposed the Washington-backed shah.

Trump's team is dedicated to reversing his predecessor's efforts at rapprochement with Iran, which saw a nuclear deal signed in 2015, lifting many sanctions.

"From Lebanon to Iraq to Yemen, Iran funds, arms and trains terrorists, militias and other extremist groups that spread destruction and chaos across the region," Trump said in Riyadh on Sunday.

He called on all countries to work together to isolate Iran "until the Iranian regime is willing to be a partner for peace".

Analysts fear tensions are growing out of control.

"Battlelines are being drawn and it's worrying, especially when it comes just a day after the election victory of Rouhani which showed a real dynamic in favour of democratisation and opening in Iranian society," said Azadeh Kian of Sciences Po University in Paris.

- 'Bastion of democracy' -

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Iran's Foreign Minister Mohammad Javad Zarif, who spearheaded the nuclear negotiations, reacted sarcastically, comparing this weekend's elections in Iran to the lack of democracy in Saudi Arabia.

"Iran -- fresh from real elections -- attacked by @POTUS in that bastion of democracy and moderation," Zarif tweeted, referring to the US president.

Is that a serious foreign policy, he asked, or is the US "simply milking" Saudi Arabia for billions of dollars?

Tehran sees itself as the vital force holding back the advance of the Islamic State jihadist group both in Syria and Iraq, and finds it hard to comprehend US bellicosity.

Shiite Iran regularly points to the Saudis' fundamentalist Wahhabi creed and their efforts to spread it around the Muslim world as the root cause of violent Sunni jihadism.

"Unfortunately, with the hostile and offensive policies of American officials, we see once again the reinforcement of terrorist groups in the region... and the dictators that support them," said Iran's foreign ministry spokesman Bahram Ghasemi on Monday.

The US and its Arab allies in the Gulf respond that Iran and Russia's support for Syrian President Bashar al-Assad has helped perpetuate the chaos.

And they say Iran's support for Lebanese militia Hezbollah and Shiite Huthi rebel forces in Yemen are deeply destabilising.

But Iran's Press TV wrote on Sunday that the aggression coming from Riyadh this weekend ultimately reflected the Saudis' realisation that they are losing in conflicts across the Middle East.

"The Riyadh regime has... failed to achieve its objectives despite going to great expense," it wrote in an editorial.