During a hostile visit to Moscow, US Secretary of State Rex Tillerson also said US-Russia ties had reached a "low point" - despite a lengthy meeting with Mr Putin and Russian foreign minister Sergei Lavrov.
During Tillerson's visit to Moscow on Wednesday, Russian Foreign Minister Sergei Lavrov gave the top USA diplomat an earful of criticism over the US strike.
Only weeks ago it seemed Trump was poised for a potentially historic rapprochement with Russian Federation.
Describing the Syrian leader as a "butcher" he said he had "absolutely no doubt" the U.S. had done the "right thing".
"It'd be a fantastic thing if we got along with Putin and if we got along with Russia", Trump said.
"It may be just the opposite".
Remarks from both sides during Tillerson's visit made clear the two countries are deeply at odds over issues including Russia's backing for Syrian President Bashar al-Assad, its interference in Ukraine, and its alleged meddling in the USA election.
Russian Federation also vetoed a United Nations resolution demanding the Syrian government cooperate with an investigation of the chemical attack, saying that Moscow had expressed its "categorical disagreement" with the draft resolution, which led to further criticism from the West, including the US.
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Russian Federation has once again denounced what it called "an act of aggression", after the United States missile strike on a Syrian airbase in retaliation to a reported use of chemical weapons in Khan Sheikhoun.
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. If Washington is colluding like that, it is better if Moscow halts the negotiations or not be so eager to welcome the Secretary of State. We're a very, very strong country.
"It is clear to us the reign of the Assad family is coming to an end", he told reporters in Italy.
Therefore, the only reasonable analysis of Putin's statement is that he is warning Assad and Iran against doing anything that could lead to more U.S. strikes against the regime which would embarrass Russian Federation, who will in turn not take any action that could lead to a military confrontation with the US.
Lavrov blasted USA claims that it has "irrefutable evidence" of election interference. We'll see. We'll see the end result, which will be in a long period of time perhaps.
"It's very important that there is a full investigation so that everybody knows, everybody knows, so that the entire world knows how these awful chemical attacks occurred and where they come from", said Delattre.
Iran's Foreign Minister Mohammad Javad Zarif on Friday called the recent United States missile attack against Syria unacceptable, media reports said.
The US ambassador, however, added that a US commitment to the peace process was "not enough" and that Washington needed "partners who are serious about using their influence" over Syrian President Bashar al-Assad. "So, I felt we had to do something about it".