Saudi Arabia reiterated Tuesday that its demands on Qatar were not negotiable, as US Secretary of State Rex Tillerson held talks with the Qatari foreign minister on the Gulf states crisis.

Saudi Foreign Minister Adel al-Jubeir, who was also in Washington, was unbudging amid attempts by US and Kuwaiti diplomats to mediate the row which has left Qatar, a US ally, isolated under a trade and diplomatic embargo set by its Gulf Arab neighbors.

"Our demands on Qatar are non-negotiable. It's now up to Qatar to end its support for extremism and terrorism," Jubeir said via Twitter.

Riyadh has laid down a list of 13 demands for Qatar, included the closure of Al-Jazeera, a downgrade of diplomatic ties with Iran and the shutdown of a Turkish military base in the emirate.

The United States though has cautioned that some of the demands would be difficult for Qatar to accept, asking the Saudis for a clear list of grievances that are "reasonable and actionable."

Shortly after Jubeir's comments, Tillerson met with Qatar's top diplomat Sheikh Mohammed bin Abdulrahman Al Thani.

He was to meet later with Kuwait Minister of State for Cabinet Affairs Sheikh Mohammad Abdullah Al-Sabah. Kuwait has taken on the official role of mediator in the spat. 

State Department Spokeswoman Heather Nauert said talks would continue through the week, but added the Saudi demands remained "challenging" for Qatar. 

"Some of them will be difficult for Qatar to incorporate and to try to adhere to," she said.

"We continue to call on those countries to work together and work this out."

Saudi Arabia, the United Arab Emirates, Egypt and Bahrain announced on June 5 they were suspending all ties with Qatar, accusing it of support for extremist groups -- a claim Doha denies.

They have also closed their airspace to Qatari carriers and blocked the emirate's only land border, a vital route for its food imports.

The move placed Washington uncomfortably in the middle, with its close economic and security ties with both sides. 

Qatar is home to the largest US base in the region, Al-Udeid. Bahrain is home to the US Navy's Fifth Fleet. 

The US and Saudi militaries work closely together as well.