Secretary of State Rex Tillerson speaks with staff at the U.S. Mission to the United Nations on Oct. 26 in Geneva. (Alex Brandon/AFP/Getty Images)

Secretary of State Rex Tillerson said Thursday that the United States wants Syria to remain one unified country and that peace talks must lead to the departure of President Bashar al-Assad.

"It's our view that we do not believe there is a future for the Assad regime, the Assad family," Tillerson told reporters in a roundtable discussion here at the end of a trip that also took him to the Middle East and South Asia. He spoke after meeting with Staffan de Mistura, the U.N. special envoy for Syria, who later announced that Syrian peace talks would resume in Geneva on Nov. 28.

"The reign of the Assad family is coming to an end," Tillerson said. "The only issue is how that should that be brought about."

Tillerson's remarks came as Syrian government troops and their Iranian-backed militia allies, with what Tillerson said was crucial support from Russian warplanes, continued to push Islamic State militants from their final strongholds in southeastern Syria. Control over the same area, near the Iraqi border, is also an objective of the Syrian Democratic Forces, U.S.-backed fighters who are trying to avoid direct conflict with the government.

The secretary said he did not see government gains "as a triumph for Iran in the defeat of ISIS," an acronym for the Islamic State. But he acknowledged that the Iranians "have somewhat taken advantage of the situation."

Assad's removal via peace talks with his political opponents has long been U.S. policy. But the timing of Tillerson's comments gave it additional emphasis as the Islamic State's grip on Syria is crumbling, the Syrian government has expanded its territorial control and negotiations are about to resume.

But after almost six years of war and 400,000 dead, the road ahead remains uncertain and riddled with strife. While the United States supports the U.N.-mediated talks in Geneva, a separate set of peace talks brokered by Russia, Iran and Turkey is already preparing for its seventh round later this month in Astana, Kazakhstan.

Tillerson's stop in Geneva was the last on a trip that took him to six other countries, some for only a few hours.

In Saudi Arabia and Qatar he urged an end to a dispute over alleged support for extremist groups that has caused four Arab countries to impose an economic blockade on Qatar. Calling for regional unity, he said the "United States remains troubled and concerned about the far-reaching consequences of the [Persian] Gulf dispute."

In Iraq, Tillerson said he encouraged the government to remain independent from Iranian influence. He said he also spoke by phone with Masoud Barzani, president of the Kurdistan Regional Government, and counseled both Barzani and Iraqi Prime Minister Haider al-Abadi to resolve their differences over the Kurdish independence push through talks based on adhering to the Iraqi national constitution.

In Afghanistan, Tillerson reaffirmed the U.S. commitment to fight the Taliban. At the same time, he said, the Trump administration has reemphasized to the Taliban that "you will never achieve a military victory" and that the door is open for a role in the Afghan government, provided its leaders "renounce terrorism."

That message, he said, has been transmitted by the administration to the Taliban "through back channels" and through the office it maintains in Doha, the Qatari capital.

His message was harsher in Pakistan, where Tillerson said he relayed the administration's expectations that Islamabad will act tougher in ridding the country of militant groups active in Afghanistan and elsewhere. If not, he said, the United States will act unilaterally.

"We're going to chart our course consistent with not just what Pakistan says they'll do, but what they do," he said.

The Pakistani reaction was not all complimentary. An editorial in Dawn, a leading newspaper, said Tillerson had "lectured" Pakistan from across two tense borders, in Afghanistan and India, and sowed resentment. But Tillerson disputed the characterization, saying he spent most of his time in Pakistan listening to officials' views.

"There's nothing to be achieved by lecturing," he said. "But we should be very clear about what we're asking."

Tillerson also stopped in India, Pakistan's traditional adversary, which the administration has said has a central role in regional peace. He said he also envisions India as a pillar of security and prosperity across the Pacific region, together with the United States, Japan and Australia.

Asked in Geneva about whether his widely reported differences with President Trump had undercut his ability to represent the administration, Tillerson said that Trump had been fully briefed on his trip and that "I'm out implementing the foreign policy that's been adopted by the president."

While in Geneva, Tillerson took a short stroll by the lake, where he stopped before a statue of several bodies curled into a tightly wound ball. A cameraman in the press pool traveling with him said he was overheard joking empathetically that sometimes he feels exactly the same way.