He has said that the Emir of Kuwait is now helping America in the Gulf and that "things are going well".
Trump, too, on Thursday offered support.
Trump also said the United States' good relations with both sides in the Israeli-Palestinian conflict could help bring about a peace agreement - what he called the "world's most complex and hard deal".
But Trump has sent conflicting signals about where he stands on the dispute. Then, he instructed Tillerson to support Kuwait's mediation, shuttling between the parties in July. Still, the dispute has dragged on for more than three months, even after Tillerson shuttled between the parties in July and dispatched two other US envoys to bolster the 88-year-old Kuwaiti emir's initiative.
The visit is in response to an invitation extended by US President Donald Trump in February, shortly after his inauguration, Shaikh Salem Abdullah Al Jaber Al Sabah told Kuwait News Agency (Kuna).
At a joint press conference with US President Donald Trump at the Oval Office on Thursday, he expressed confidence in the "wisdom of our brothers in the Gulf", particularly when taking into account other regional developments in Syria, Iraq and Libya.
Sheikh Sabah claimed that the Qatari government was ready to discuss a list of 13 demands from its Arab neighbors.
But underscoring the impasse, the quartet of Arab nations boycotting Doha issued a strongly worded statement early Friday morning dismissing some of the emir's comments.
Saudi Arabia and its Arab satellite states of Bahrain, Egypt, and the United Arab Emirates cut their diplomatic ties with Qatar on June 5, accusing Doha of sponsoring terrorism and destabilizing the region.
The meeting will address bilateral relations and regional and worldwide developments of mutual interest, and cooperation in the fight against terror will figure high on the summit's agenda, the envoy said, stressing that Kuwait is a major partner to the USA in the war on terror.