US Secretary of State Rex Tillerson has arrived in Doha for talks with Qatar's emir and foreign minister on the second leg of his four-day trip to the Gulf to help seek a resolution to the ongoing GCC crisis.

The US State Department said Tillerson would first meet with Emir Sheikh Tamim bin Hamad Al Thani on Tuesday, before holding talks with Foreign Minister Sheikh Mohammed bin Abdulrahman Al Thani.

The visit to Doha follows a meeting with the Emir of Kuwait, Sheikh Sabah al-Ahmad al-Sabah and other senior Kuwaiti officials on Monday.

"We are trying to resolve an issue that concerns not just us but the whole world," Sheikh Sabah told Tillerson.

US officials said Tillerson does not expect an immediate breakthrough, which they warned could be months away.

Rather, they said, he wants to explore possibilities for sparking negotiations.

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

The quartet accuse Qatar of funding "terrorism", an accusation Qatar rejects as "baseless".

On June 22, they issued a 13-point list of demands, including the shutdown of Al Jazeera, limiting ties with Iran and expelling Turkish troops stationed in the country, as a prerequisite to lift the sanctions.

Doha rejected the demands and the countries now consider the list "null and void".

Kuwait is still trying to mediate the dispute.

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The US has been supporting Kuwait's mediation efforts, but Tillerson's trip marks a new level of US involvement.

Al Jazeera's Rosiland Jordan, reporting from Kuwait City, said Tillerson was basically visiting each side to "take the temperature in this dispute".

"After some initial missteps from the White House, in which the president seemed to take sides with the Saudis and their allegations, the US' position now is to try to shore up the Kuwait efforts to mediate the crisis and to try to bring some presure from Washington, if it's appropiate," she said.

Senior Tillerson adviser R.C. Hammond said the package of demands, as issued by Qatar's neighbours, was not viable, but said there were individual items on the list "that could work".

Hammond would not elaborate on which demands Qatar could meet, but said concessions from the others would be required.

"This is a two-way street," he said of a dispute among parties who each have been accused of funding "extremists" in some way. "There are no clean hands."

On Thursday, the state department warned that the crisis could potentially drag on for weeks or even months and "possibly even intensify".

"We've become increasingly concerned that that dispute is at an impasse at this point. We believe that this could potentially drag on for weeks; it could drag on for months; it could possibly even intensify," state department spokeswoman Heather Nauert said.

She did not specify what type of escalation the US fears. But she said Tillerson has been in close contact with the countries involved.

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Last month, Tillerson urged the Saudi-led group to ease their blockade on Qatar, saying it is causing unintended humanitarian consequences and affecting the US-led fight against the Islamic State of Iraq and the Levant (ISIL, also known as ISIS) group.

"Our expectation is that these countries will immediately take steps to de-escalate the situation and put forth a good faith effort to resolve the grievances they have with each other," Tillerson said.

More than 11,000 US and coalition forces are stationed at the Al Udeid Air Base in Qatar, from which more than 100 aircraft operate.