GENEVA — Secretary of State Rex W. Tillerson said Thursday that President Bashar al-Assad of Syria must not remain in power, but that negotiations about the country’s future should continue while Mr. Assad was in charge.

“The United States wants a whole and unified Syria with no role for Bashar al-Assad in the government,” Mr. Tillerson told reporters, adding, “The reign of the Assad family is coming to an end. The only issue is how that should that be brought about.”

The comments came after Mr. Tillerson met in Geneva with the United Nations special envoy on the Syrian crisis — the last stop on a weeklong visit to the Middle East and South Asia in which he dashed among capitals in the region, often spending only a few hours on the ground before getting back into his motorcade and heading to the next stop.

While he came home with no major accomplishments, the trip was also not interrupted by tweets from President Trump contradicting his efforts, as happened early this month with the secretary’s efforts on North Korea.