Whether Mr. Tillerson’s tough stance on Russia is in keeping with Mr. Trump’s often-stated wish to improve relations with Russia is unclear. But the secretary of state has maintained it since his confirmation hearings in January despite the Order of Friendship he had received from Mr. Putin when Mr. Tillerson was Exxon Mobil’s chief executive.
Mr. Tillerson and Mr. Trump disagree on a host of important policies, including climate change and Iran, and their differences in tone regarding Russia are striking. Such variances are an important reason that senior administration officials said on Thursday that the White House planned to replace Mr. Tillerson with Mike Pompeo, director of the Central Intelligence Agency, who is more closely aligned with Mr. Trump’s nationalistic views.
So far, however, Mr. Tillerson has shown no signs he is willing to leave quietly — all but daring the president to fire him.
After his talks with Mr. Putin in November on the sidelines of the Asia-Pacific Economic Cooperation summit meeting in Danang, Vietnam, Mr. Trump emphasized that he believed Mr. Putin was sincere in his denials of interference in the 2016 United States presidential elections, an assessment that was widely condemned.
Mr. Trump later posted on Twitter, “When will all the haters and fools out there realize that having a good relationship with Russia is a good thing, not a bad thing.”
In Vienna, Mr. Tillerson did not mention election meddling, saying the two countries’ differences over Crimea and Ukraine were the true sticking points.
“President Trump, as you know, throughout his campaign was very clear that he views it as very important that Russia and the United States have a better relationship, but the issue that stands in the way is Ukraine,” Mr. Tillerson said at a news conference with the Austrian foreign minister, Sebastian Kurz.
For the first time in months, Mr. Tillerson had much of the Western world on his side, with diplomats from Canada, countries in Europe and other nations pledging support for his efforts to hold Russia to account.
The Trump administration’s withdrawal from the Paris climate accord, threats to leave the Iran nuclear agreement and the president’s declaration on Wednesday acknowledging Jerusalem as Israel’s capital have created stark divisions between Washington and nearly all of its traditional allies.
During Mr. Tillerson’s first two days in Europe this week, those differences were inescapable, as every one of his counterparts in the European Union and NATO denounced one or more of Mr. Trump’s moves, often while standing next to Mr. Tillerson.
Such isolation has become the theme of the secretary of state’s tenure, as the White House freezes him out of policymaking, allies treat him coldly and his diplomatic corps views him as something of a pariah because of his tendency to ignore them.
With the Russians in Vienna, though, Mr. Tillerson was no longer the outsider, and Washington’s traditional allies rallied around him.
The main focus of the security forum is a proposal to deploy a United Nations peacekeeping force to Eastern Ukraine. Moscow and Washington support such a mission but differ on its details. Washington wants the force to have a broad mandate to help end the fighting and restore Ukrainian sovereignty.
“We will continue to work with Russia to see if we cannot agree on a peacekeeping force that can enter Ukraine, reduce the violence,” Mr. Tillerson said, adding, “More people have died in 2017 than 2016, and this simply has to stop.”
But while Russia wants the peacekeepers’ mandate to be narrowly drawn to protect international monitors, the United States says it believes such a mandate would serve only to solidify Russia’s intervention. One monitor, an American paramedic, was killed in April.
Mr. Lavrov said the United States intended to create “an occupational administration” and “to solve this problem by force.”
The war in Eastern Ukraine began in 2014, when Russia secretly sent troops into the area to support separatists. More than 10,000 people have since died there.
After their tough speeches, Mr. Tillerson and Mr. Lavrov held a bilateral meeting Thursday afternoon, and a crush of Russian journalists rushed in, along with a few American reporters, in hopes that Mr. Lavrov would engage in the kind of playful banter for which he is famous.
After an American reporter shouted a question to him about Mr. Trump’s decision on Jerusalem, Mr. Lavrov told the reporter to shout louder. She did, her words echoing around the small salon like a tuba from an Austrian oompah band.
“I can’t hear you,” the Russian envoy said, and the news media was ushered out.
After the meeting, Mr. Tillerson said there had been progress with the Russians.
“We get dialogue, we get cooperation,” he said. “We don’t have it solved. You don’t solve it in one meeting.”