US Secretary of State Rex Tillerson and Qatari Foreign Minister Sheikh Mohammed bin Abdulrahman Al-Thani made the announcement at a joint news conference in Doha.
This comes at a time when Qatar is facing sanctions from neighbouring countries, for allegedly supporting terrorism.
Saudi Arabia, Bahrain, UAE and Egypt cut diplomatic ties with Qatar on June 5, accusing Doha of financing extremist groups and allying with Iran.
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Qatar had since denied the allegations adding that the boycott was part of a campaign to rein in its independent foreign policy.
Speaking on the month-old diplomatic row, Tillerson said Qatar had “reasonable” views with Arab neighbours.
“I am hopeful we can make some progress to begin to bring this to a point of resolution.
“I think Qatar has been quite clear in its positions, and I think those have been very reasonable,” the US top Diplomat said.
The U.S. worries is that the crisis could impact its military and counter-terrorism operations and increases the regional influence of Iran, which has been supporting Qatar by allowing it to use air and sea links through its territory.
Tillerson and British National Security Advisor Mark Sedwill had met on Monday with officials from Kuwait, which is acting as a mediator, in order to patch up the row among the Western-allied countries.
The State Department said Tillerson was also expected to travel to Saudi Arabia.