Washington (dpa) - US President Donald Trump says he has directed the Treasury Department to "substantially increase" sanctions on Iran following the weekend attacks on Saudi oil facilities.

"I have just instructed the Secretary of the Treasury to substantially increase Sanctions on the country of Iran!" Trump wrote in a tweet on Wednesday.

It was not immediately clear what specific actions Trump had ordered Treasury Secretary Steven Mnuchin to take.

Washington has ratcheted up its "maximum pressure" campaign on Iran, which it began after pulling out of the 2015 nuclear deal with Iran and reinstating hard-hitting oil and financial sanctions.

In has also recently announced sanctions against the country's Supreme Leader Ali Khamenei, Foreign Minister Mohammad Javad Zarif and labelled Iran's elite Revolutionary Guard Corps as a foreign terrorist organization.

The Trump administration wants a broader deal that goes beyond nuclear issues and discusses Iran's ballistic missile programme and role in regional conflicts.

Tensions have mounted for months between Iran and the West after a series of fuel tankers were seized and Iran began rolling back its compliance with the nuclear accord.

However, the drone attack on the Saudi facilities marked a dramatic escalation in the confrontation, sparking oil supply concerns and fears of an outbreak of fighting between the US and Iran.

The attack, claimed by Yemen’s Iran-linked Houthi rebels, struck major Saudi oil installations. Saudi Arabia and the US have blamed the attack on Iran, although Iran denies the charges.

US Secretary of State Mike Pompeo was due in Saudi Arabia on Wednesday to discuss a potential response with Saudi leaders.

Iranian President Hassan Rowhani earlier Wednesday said Iran would consider talks with the United States only if Washington shows "goodwill" and by offering sanctions relief.

There has been speculation for weeks that Rowhani could hold talks with Trump on the sidelines of the UN General Assembly in New York next week.

But after the events at the weekend it is now unclear whether the Iranian delegation will be granted permission to enter the US. According to the Iranian Fars news agency, Rowhani has not yet received a visa to attend the General Assembly, the UN's biggest annual diplomatic event.