Saudi Arabia, Bahrain, UAE and Egypt imposed sanctions last month, accusing Qatar of financing extremist groups and allying with Iran, the Gulf Arab states' arch-foe, something it denies.
"I am hopeful we can make some progress to begin to bring this to a point of resolution," Tillerson said alongside his Qatari counterpart Sheikh Mohammed bin Abdulrahman al-Thani.
"I think Qatar has been quite clear in its positions, and I think those have been very reasonable," Tillerson said.
The United States worries the crisis could impact its military and counter-terrorism operations and increase the regional influence of Iran, which has been supporting Qatar by allowing it to use air and sea links through its territory.
Qatar denies that it supports militant organisations and says the boycott is part of a campaign to rein in its independent foreign policy.
Following those discussions, the United States, Britain and Kuwait urged all parties to resolve their dispute quickly through dialogue, Kuwait state news agency KUNA reported.
Coming from some of the most influential powers in the dispute, the plea for a negotiated solution may be aimed at an earlier refusal by Qatar's adversaries to discuss renewing ties with Doha until it first acquiesced to a list of demands, including closing the Al Jazeera TV channel, shutting a Turkish military base in Qatar and downgrading ties with Iran.
Qatar hosts Udeid Air Base, the largest U.S. military facility in the Middle East, from which US-led coalition aircraft stage sorties against Islamic State in Syria and Iraq.
US President Donald Trump has expressed support for Saudi Arabia in the dispute.