Mr. Tillerson made clear Friday that the end of the blockade of Yemeni ports must include commercial shipments, not just humanitarian ones, “because about 80 percent of the food comes in on commercial ships.”
He met Friday with Prime Minister Saad Hariri of Lebanon and President Emmanuel Macron of France. Mr. Macron’s invitation to Mr. Hariri to visit Paris in November after Mr. Hariri shocked his country by offering his resignation while visiting Saudi Arabia was the first step in unwinding the crisis.
Western countries have since pledged to help Lebanon protect itself from other regional crises.
In a speech Friday, Mr. Hariri thanked Mr. Macron for his support of Lebanon.
“Lebanon has just been through a crisis that could have affected its political, economic and security stability,” Mr. Hariri said. “It escaped thanks to its friends, many of whom are here, and to the will of its people and its representatives not to succumb to it.”
The Saudis pushed Mr. Hariri to resign in an effort to reduce Iran’s influence in the country, but the ham-handed effort backfired, leading Lebanese and Western countries to rally to Mr. Hariri’s defense.
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“I think as to Lebanon, things have worked out in a very positive way,” Mr. Tillerson said, “perhaps even more positive than before because there have been very strong statements of affirmation for Lebanon, which will only be helpful.”
Also on Friday, Mr. Tillerson said that opening an American embassy in Jerusalem, now officially regarded by the Trump administration as Israel’s capital, will take years. Many countries have castigated Mr. Trump’s decision on Jerusalem as a violation of United Nations resolutions.
“This will take some time,” Mr. Tillerson said. Citing land acquisition and construction demands, he said much work remains. “So this is not something that’s going to happen this year, probably not next year,” he said.
Whether Mr. Tillerson’s mild criticism of the Saudis signals a broader reassessment by the Trump administration of the relationship with Saudi Arabia is far from clear. Mr. Tillerson is widely believed to have a difficult relationship with Mr. Trump, and the two have admitted to a host of differences on key policy questions.
The New York Times reported last week that Chief of Staff John F. Kelly had a plan to force out Mr. Tillerson, one widely believed to have the backing of Jared Kushner, Mr. Trump’s son-in-law. The White House disputed the report.
Mr. Kushner has developed a close relationship with the Saudi crown prince, Mohammed bin Salman, and Mr. Kushner’s efforts to forge a Middle East peace between the Israelis and Palestinians are thought to include important contributions from Prince Mohammed.
Mr. Tillerson and the State Department have largely been excluded from these efforts, with Mr. Tillerson more skeptical of Mr. Kushner — a skepticism that, in the aftermath of the botched Saudi move that jolted Lebanon, looks prescient.
If the White House’s ardor for Saudi Arabia has cooled, the Trump administration will be following a pattern forged by most of its modern predecessors. Past American presidents have come into office enthusiastic about improving ties with Saudi Arabia, only to experience considerable disappointment.
An earlier version of this article incorrectly depicted the circumstances surrounding a plan to replace Rex W. Tillerson as secretary of state. The New York Times reported on the plan; it was not announced by the White House.