US Secretary of State Rex Tillerson told reporters in Doha that the Qatari government had "reasonable" views in the month-old diplomatic crisis with Arab neighbours.

"I think Qatar has been quite clear in its positions, and I think those have been very reasonable," Tillerson said after his arrival in Doha on Tuesday.

A Saudi-led quartet of countries accuse Qatar of funding "terrorism", an accusation Qatar rejects as "baseless".

In a joint news conference, Tillerson and the Qatari foreign minister announced that the US and Qatar made an agreement on combating "terrorism" and its financing during the visit.

Foreign Minister Sheikh Mohammed bin Abdulrahman Al Thani said the memorandum of understanding has nothing to do with the current dispute.

Tillerson also held talks with Qatar's Emir Sheikh Tamim bin Hamad Al Thani on the second leg of his four-day trip to the Gulf to help seek a resolution to the crisis.

ANALYSIS: Qatar-Gulf crisis - Who are the 'terrorists'?

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.

On Wednesday, Tillerson will meet the foreign ministers of the countries leading the boycott against Qatar - Saudi Arabia, the United Arab Emirates, Bahrain and Egypt - in Jeddah.

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 UAE, Bahrain and Egypt cut ties with Qatar on June 5 and imposed a land, air and sea blockade on the country.

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.

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

READ MORE: Qatar-Gulf crisis - All the latest updates

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 pressure from Washington, if it's appropriate," she said.

Senior Tillerson adviser RC 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."