Tillerson made the comments after meeting with Qatar's Emir Sheikh Tamim bin Hamad Al-Thani and the country’s foreign minister in Doha on Tuesday.
"I'm hopeful we can make some progress to bring this to a point of resolution," he said after meeting the Qatari emir.
"I think Qatar has been quite clear in its positions and I think very reasonable and we want to talk now... how do we take things forward, and that's my purpose in coming."
The top US diplomat traveled to Qatar as part of his Persian Gulf tour to break the five-week rift between Doha and several Arab states.
Ahead of his Doha visit, Tillerson made a stop in Kuwait, which is still trying to mediate the dispute.
Tillerson will visit Saudi Arabia before leaving the Persian Gulf region on Thursday. He will hold a meeting with the foreign ministers of the four countries involved in the dispute on Wednesday in Riyadh.
[caption id="" align="alignnone" width="550"]
Kuwaiti Foreign Minister Sheikh Sabah al-Khaled al-Sabah (C) meeting with US Secretary of State Rex Tillerson (R) and UK National Security Adviser Mark Sedwill (L) during talks at Bayan Palace in Kuwait City, July 10, 2017. (Photo by AFP)[/caption]The US State Department has warned the crisis could last months and Tillerson does not expect to produce a breakthrough, but instead, wants to explore possibilities for bringing all sides to the negotiating table.
The unprecedented crisis in the Persian Gulf region unfolded on June 5, when Saudi Arabia, Bahrain, the United Arab Emirates and Egypt cut off diplomatic ties with Qatar and placed an air, land and sea embargo on the country over claims that Doha supports terrorism.
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On June 22, the four Arab states issued a 13-point list of demands as a prerequisite to lift the sanctions against Qatar.
Qatar has denied the terrorism allegations, calling the list of demands and the embargo unjustified and a violation of international law.
Many experts say Saudi Arabia sparked the diplomatic conflict to rein in Qatar’s increasingly independent foreign policy.
The split among the Arab states erupted in May after US President Donald Trump visited Saudi Arabia and then pointing out that numerous Arab leaders had complained to him that Qatar is supporting terrorism.
Saudi Arabia was the first stop on Trump's first international trip on May 20. No other US president has made the kingdom their first foreign visit.
Analysts said Trump’s public support for Saudi Arabia emboldened the regime to adopt a more hawkish regional diplomacy.
Tillerson's visit is the latest in a series by officials to the region, including UN diplomats and the foreign ministers of Britain, Germany and Oman. The United States and its Western allies have vast economic and political interests in the region.
Qatar, the world's biggest exporter of liquefied natural gas, hosts about 10,000 US troops at its al-Udeid Air Base.
