Giving Tillerson a chilly reception, Russian Foreign Minister Sergey Lavrov said Russia was trying to understand the "real intentions" of the Trump administration.
He said Moscow has lots of questions about the "very ambiguous" and "contradictory" ideas emanating from Washington.
"We have seen very alarming actions recently with an unlawful attack against Syria," Lavrov said, referring to the cruise missiles President Donald Trump ordered to punish Assad for using chemical weapons. "We consider it of utmost importance to prevent the risks of replay of similar action in the future."
"We both have agreed our lines of communication shall always remain open," Tillerson said.
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The palpable tension hanging over Tillerson's trip spoke to a widening chasm between the former Cold War foes.
Only weeks ago, it appeared that Trump, who lavishly praised Putin throughout the campaign, was poised for a potentially historic rapprochement with Russia. But any expectations of an easy rapport have crashed into reality as the two countries trade escalating accusations over what happened last week in rebel-held territory in northern Syria.
"Frankly, Putin is backing a person that's truly an evil person," Trump told the Fox Business Network, referring to Assad. "I think it's very bad for Russia. I think it's very bad for mankind."
Of Assad, Trump added: "This is an animal."
And Putin, who US intelligence agencies say tried to help Trump get elected, insisted that relations with the US had only gone downhill since Trump took office in January.
"The level of trust at the working level, especially at the military level, has not become better but most likely has degraded," Putin said in an interview broadcast today by state television channel Mir.
Moscow has strenuously objected to Trump's decision to launch 59 US Tomahawk missiles at a Syrian air base that the US says was used to pummel civilians with nerve gas, killing more than 80 people. Russia, Assad's staunchest ally, has insisted that Assad is blameless and that it was actually the rebels responsible for the disbursed chemical weapons.
Adding further fuel to rising tensions: the White House's move to circulate declassified US intelligence accusing Moscow of aiding Assad's government in covering up the chemical attack. The US also accused Russia of mounting a disinformation campaign aimed at exonerating Assad.
Tillerson, on a mission to persuade Russia to abandon Assad, issued an ultimatum to Putin before flying to Moscow: Either side with the US and likeminded countries, or with Assad, Iran and the militant group Hezbollah.
"Our policy is consistent and it's formulated exclusively on the basis of international law and not under the impact of current opportunistic motives or false choice: 'You are with us or against us,'" Lavrov told Tillerson.
The Trump administration's growing willingness to confront Russia directly is serving another purpose: defanging the perception of coziness between Trump and Moscow.
As the FBI and multiple congressional committees investigate potential collusion between Russia and Trump's campaign in last year's US election, Trump can point to his hard-line stance as fresh evidence that he's far from beholden to the Russian leader.
He was referring to widespread vacancies throughout the top State Department leadership that has fueled a perception in the US that Tillerson and his agency are being sidelined by Trump.
"It's not easy to get clarifications on the current as well as prospective issues because of that," Lavrov said.
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