US Secretary of State Rex Tillerson has called for direct talks between Saudi Arabia-led group and Qatar, as he wrapped up a four-day mission to solve the Gulf crisis.

Before leaving for Washington, Tillerson returned to Doha on Thursday to meet Qatar's Emir Sheikh Tamim bin Hamad Al Thani for the second time in 48 hours, together with a Kuwaiti mediator.

"Based on his meetings, the secretary believes that getting the parties to talk directly to one another would be an important next step," US State Department spokesman Heather Nauert said on Thursday.

"We look forward to that happening," she said without giving a specific timeline.

Despite an intense round of shuttle diplomacy that also took him to Kuwait and Saudi Arabia, tensions remain high between Qatar and four Arab states that accuse Doha of funding "terrorism" and is being too close to Iran - allegations Qatar has repeatedly denied.

Saudi Arabia, the United Arab Emirates, Bahrain and Egypt imposed a land, sea and air blockade on Qatar on June 5.

Al Jazeera's Hashem Ahelbarra, reporting from Doha, said officials do not expect the crisis to end in the near future.

"Qatar's foreign minister and the Kuwaiti mediator seem to have been exploring new ideas that could be the framework for any future deal, but we've been told that it's not happening any time soon," he said.

"Tillerson has left Doha but the Qatari government officials' stance remains that they won't negotiate anything unless the embargo is lifted. At the same time, they are open to anything that is not considered infringing on their sovereignty."

Tillerson's clearest achievement has been to secure a memorandum of understanding with Qatar to strengthen its counterterrorism efforts.

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"Since Qatar signed the memorandum of understanding with the US, newspapers owned by Saudi Arabia and the UAE have lashed out at Tillerson, blaming him to be leaning towards Qatar and describing the shuttle diplomacy as something that is not going to come up with any tangible results," Ahelbarra said.

French Foreign Minister Jean-Yves Le Drian is expected to arrive in the region over the next few days.

The anti-Doha quartet is holding fast to its insistence that Qatar bow to a 13-point list of demands that includes shutting down Qatar's Al Jazeera Media Network, sever all alleged ties with the Muslim Brotherhood and with other groups, including Hezbollah, al-Qaeda and ISIL (also known as ISIS), limiting Qatar's ties with Iran and expelling Turkish troops stationed in the country.

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Qatar denies the charges of extremism and called the demands "unrealistic".

On Thursday, a human rights group said abuses were caused by the Saudi-led group's blockade.

"Hundreds of Saudis, Bahrainis, and Emiratis have been forced into the impossible situation of either disregarding their countries' orders or leaving behind their families and job," said Sarah Leah Whitson of Human Rights Watch.

The US and its Western allies have vast economic and political interests in the Gulf, which pumps one fifth of the world's oil supplies.