But Trump did not seem to change in his assessment of Russian President Vladimir Putin, who Trump has spoken of admiringly in the past.
Meanwhile, Tillerson said that he and Lavrov discussed Syrian President Bashar al-Assad at length and that he made clear that the Trump administration has come around to the view that the Syrian President can not stay in power.
Of Assad, Trump added: "This is an animal".
The vote comes after a meeting between US Secretary of State Rex Tillerson and Russian minister Sergey Lavrov in Moscow to talk about the Syrian situation.
"You can say that the level of trust on a working level, especially on the military side, has not improved but most likely worsened", Putin said in the transcript of an interview with Mir television released by the Kremlin.
Russian President Vladimir Putin says relations between Moscow and Washington have deteriorated in the early months of Donald Trump's presidency.
Tillerson will fly back to the United States tomorrow but says both are committed to talking about their significant differences.
"The world's two foremost nuclear powers can not have this kind of relationship", he said.
Hillary Clinton chides Donald Trump on Syrian refugee ban after airstrikes
Given the recent events over the past twenty-four hours, it's expected that Clinton will comment on President Trump's overnight military strike in Syria.
The United States has implicated the Assad government in crimes against humanity, including attacks on civilians with chemical weapons.
The tests were not part of an official investigation launched by the Organization for the Prohibition of Chemical Weapons in the wake of the attack. Syria and Russian Federation have said the chemicals belonged to "terrorists".
Tillerson reiterated that Assad was behind the attack.
The text also condemned the reported use of chemical weapons and demanded a speedy investigation.
The two did outline some areas of agreement Wednesday. He said it was "unacceptable that the OPCW analyses the evidence not on location". However, this appears impossible with the recent confrontations between the countries over Syria, and the ongoing investigations of Russia's alleged interference in the United States presidential elections. But Tillerson repeated the administration's new belief that "the reign of the Assad family is coming to an end".
WATCH: Can Russia abandon Assad?
"We both believe in a unified and stable Syria", Tillerson said.
Assad said on Thursday the alleged poison gas attack in Khan Sheikhoun was a "fabrication" to justify a USA military strike. "With the acts that [Assad] has taken, it would seem that there would be no role for him to govern the Syrian people".
Increased concerns among NATO's European states about Russian military activity on its eastern flank fed into a question to Trump about strained ties with Russia. Lavrov, however, pointed to the downside of removing a foreign leader. "We know the ending of it way too well".