Saudi forces keep watch along the border with Yemen from where there have been repeated rebel missile attacks on the kingdom since November

The United States called Tuesday for international action to hold Iran to account after Saudi Arabia accused Tehran of "direct military aggression" over a Yemeni rebel missile attack near Riyadh.

The Iran-backed Huthi rebels also threatened to attack ports and airports in Saudi Arabia and the United Arab Emirates, escalating a crisis between Riyadh and Tehran.

Saudi Arabia's powerful crown prince had accused Iran of supplying missiles to the Huthis, which he said "could be considered as an act of war".

Iranian Foreign Minister Mohammad Javad Zarif retorted that "the allegations by Saudi officials were contrary to reality", a foreign ministry spokesman said.

Washington's ambassador to the United Nations, Nikki Haley, said Tuesday that Iran had supplied a missile to the Huthis that was fired into Saudi Arabia in July, and referred to Riyadh's claim that the weapon used on Saturday "may also be of Iranian origin".

"By providing these types of weapons to the Huthi militias in Yemen, Iran's Islamic Revolutionary Guard Corp‎s is violating two UN resolutions simultaneously," Haley said.

"We encourage the United Nations and international partners to take necessary action to hold the Iranian regime accountable for these violations."

Saudi Arabia and Iran back opposing sides in wars and power struggles from Yemen to Syria.

Soaring tensions between the key oil producers pushed crude closer to two-year highs on Tuesday and spooked Gulf markets.

Europe's top diplomat Federica Mogherini warned the mounting tension was "extremely dangerous", and urged Riyadh and Tehran to seek a "minimum of common ground" on which to build peace.

"I know that this is not the wind that is blowing as the majority voice in the world of today," Mogherini told reporters at the EU mission in Washington.

"But allow me to bring a little bit of wisdom as the European voice in a world that seems to go completely crazy here: It's dangerous."

Saturday's attack showed that despite a more than two-year Saudi-led bombing campaign and blockade, the Huthis retain missiles capable of striking targets deep inside the kingdom.

The rebels' warned that they considered Saudi and UAE "airports, ports, border crossings and areas of any importance" as legitimate targets.

"We will not stand idly by -- we will seek more radical means to prevent both the tightening of the blockade and all acts aimed at starving and humiliating the people of Yemen," the Huthis' political office said.

The missile, intercepted and destroyed near Riyadh international airport, was the first to reach the Saudi capital and underscored the growing fallout for Saudi Arabia and its UAE ally from their involvement in neighbouring Yemen.

The two are the major powers in a coalition that has been fighting the Huthis since 2015 in support of the internationally recognised government.

Since Saturday's attack, the coalition has tightened its blockade of rebel-held areas of Yemen, blocking UN-supervised aid deliveries despite urgent appeals from the world body.

The coalition said it aimed to fill gaps in inspection procedures that enable "smuggling of missiles and military equipment" to the rebels.

- 'Catastrophic' blockade -

But the blocking of aid threatens some seven million people already on the brink of famine.

The UN urged the coalition to lift the blockade as soon as possible.

"If these channels, these lifelines, are not kept open it is catastrophic for people who are already in... the world's worst humanitarian crisis," said Jens Laerke, a spokesman for the UN's humanitarian coordination office (OCHA) in Geneva.

OCHA said the coalition had also asked it to clear ships from the rebel-held Red Sea port of Hodeida, a key entry point for UN aid.

Laerke said fuel prices in rebel-held areas had jumped by up to 60 percent and cooking gas prices had doubled.

The International Committee of the Red Cross also urgently called for humanitarian access to be restored.

"Humanitarian supply lines to Yemen must remain open," said Robert Mardini, who heads ICRC's Near and Middle East operations.

"Food, medicine and other essential supplies are critical for the survival of 27 million Yemenis already weakened by a conflict now in its third year."

Saudi Arabia is also embroiled in the biggest purge of the kingdom's elite in its modern history.

Dozens of high-profile figures including princes, ministers and billionaire tycoon Al-Waleed bin Talal were swept up in the weekend purge -- just after the creation of an anti-graft commission headed by Prince Mohammed.

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