The visit is Tillerson's second stop on a shuttle diplomacy tour aimed at resolving the ongoing diplomatic crisis in the Gulf region.
US Secretary of State Rex Tillerson landed in Qatar on Tuesday on a mission to break the deadlock between the tiny, energy-rich Gulf nation and four Arab neighbours that is seriously straining relations among the American allies.
The visit is Tillerson's second stop on a shuttle diplomacy tour that is also expected to take him to Saudi Arabia, which shares Qatar's only land border and is the most powerful of the four countries lined up against it.
TRT Worlds's Soraya Lennie reports from Doha.
The diplomat, a former oilman with years of experience in the region, held talks with Kuwait's ruling emir, Sheikh Sabah al Ahmed al Sabah, during his first stop in the Gulf on Monday evening.
The Kuwaiti leader has been acting as a mediator between Qatar and the quartet of Saudi Arabia, Bahrain, the United Arab Emirates and Egypt.
The four nations broke off relations with Qatar and cut air, sea and land routes with it in early June and have accused Qatar of supporting extremist groups. They later issued a 13-point list of demands to restore relations and gave Doha 10 days to comply.
The demands include Qatar shutting down news outlets, including the media network Al Jazeera, cutting ties with groups such as the Muslim Brotherhood, limiting ties with Iran and expelling Turkish troops stationed in the country.
Qatar strenuously denies supporting extremist groups and has rejected the demands, saying that agreeing to them wholesale would undermine its sovereignty.
US officials have said Tillerson does not expect an immediate breakthrough in the dispute and cautioned that a resolution could take months.
A senior adviser to Tillerson, RC Hammond, has said the demands on Qatar were not viable but that there were individual items on the list "that could work." He did not elaborate.
Qatar is not new territory for Tillerson. Before being tapped to be President Donald Trump's top diplomat, he served for years as CEO of Exxon Mobil.
The Irving, Texas-based oil giant is one of the most dominant players in OPEC, or Organization of the Petroleum Exporting Countries.
Qatar's energy industry has played a major role in turning it into the world's largest producer of liquefied natural gas.