Mr Tillerson is due to meet his Russian counterpart, Sergei Lavrov, in Moscow on Tuesday.
Turkey has long said Syria has no future under the Bashar al-Assad regime, while Russian Federation has come to the Syrian regime's aid.
The missile strikes were the first time the United States has directly targeted al-Assad's forces in the six-year war.
The top Russian and Iranian generals have condemned the USA missile strike against a Syrian military base and vowed to continue their fight against "terrorists", which they generally call opponents of Syrian President Bashar al-Assad.
Russian President Vladimir Putin said he has intelligence that the USA has planned similar missile strikes to last week's on a Syrian military base, including plans to strike the capital Damascus, according to comments carried by state media Tuesday.
Taken together, the comments of Haley and Tillerson suggested senior members of Trump's foreign policy team may be seeking to shape the president's views, with Haley more opposed than Tillerson to Assad remaining in power.
President Donald Trump ordered the missile strike after watching television images of infants suffering from chemical weapons injuries. Secondly, we don't see a peaceful Syria with Assad in there.
Russian Federation is the Syrian government's main ally, and helped facilitate a 2013 agreement to destroy Syria's chemical arsenal.
Trump administration officials on Sunday blamed Russian inaction for enabling a deadly poison gas attack against Syrian civilians last week as Secretary of State Rex Tillerson prepared to explain to Moscow a US retaliatory missile strike.
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The race card is just a convenient excuse for Zuma to ignore his detractors. Rather, it was about South Africa and the mobilisation of the citizens.
While Nikki Haley, the US ambassador to the United Nations, described regime change in Syria as a USA priority and inevitable, Tillerson suggested that last week's American airstrikes in retaliation for the chemical attack hadn't really changed USA priorities toward ousting Assad.
USA secretary of state Rex Tillerson is then expected to deliver a message that the Kremlin faces worldwide isolation if it stands by the regime in Damascus.
Mr Johnson's visit, for talks with his Russian counterpart Sergey Lavrov, would have been the first by a United Kingdom foreign secretary in more than five years.
Air strikes have struck Syria's town of Urum al-Joz in rebel-controlled Idlib province on Saturday, according to the Syrian Observatory for Human Rights and the Civil Defence rescue service.
The US ambassador to the United Nations has said America is "prepared to do more" militarily in Syria but hopes it will not be necessary.
The US officials said Russian commanders in Syria were informed of the strike beforehand in order to avoid casualties that could prompt a broader crisis.
"Someone who uses barrel bombs and chemicals to kill his own people simply can not be the future leader of Syria", he stated.
Moscow has further promised to strengthen Syria's anti-aircraft defences and it is shutting down a hotline with the USA created to avoid collisions between their air forces over the country. The Syrian government has denied it was behind the attack.