Mr Tillerson told Tillerson told reporters while commemorating a German Nazi massacre committed in Sant'Anna di Stazzema, Italy in 1944: "We rededicate ourselves to holding to account any and all who commit crimes against the innocents anywhere in the world."
The US attacked the Syrian air base in retaliation for what it said was a chemical weapons assault by Syrian President Bashar al-Assad that killed dozens of civilians, including many children.
Mr Tillerson is in Italy for a meeting of foreign ministers from the Group of Seven (G7) major industrialised nations, with his counterparts from Europe and Japan eager for clarity from Washington on numerous diplomatic issues, especially Syria.
Rex Tillerson (centre)
Before the April 7 missile strikes on a Syrian airbase, US President Donald Trump had indicated he would be less interventionist than his predecessors and willing to overlook human rights abuses if it was in US interests.
US Secretary of State Rex Tillerson has said its military strike against Syria over its alleged use of chemical weapons was a warning to other countries including North Korea that "a response is likely" if they pose a danger.
He said on CBS's Face the Nation: "(Chinese) President Xi (Jinping) clearly understands, and I think agrees, that the situation has intensified and has reached a certain level of threat that action has to be taken."
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Rex Tillerson, the former CEO and chairman of ExxonMobil Corporation, is Donald Trump‘s Secretary of State
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Commenting on US missile strikes against Syria last week, Peskov told reporters today the action had shown Washington's total unwillingness to cooperate on Syria.
He said renewed calls for Syrian President Bashar al-Assad to step down would not help to resolve the crisis.
Mr Peskov said: ”There is no other alternative," to peace talks in Geneva and Astana.
Mr Trump ordered his military to strike Syria in retaliation for what the United States said was a chemical weapons attack by President Bashar al-Assad's forces which killed scores of civilians, including many children.
European ministers are eager to hear whether Washington is now committed to overthrowing Mr Assad, who is backed by Russia. They also want the United States to put pressure on Moscow to distance itself from Assad.
Mr Tillerson, who travels to Russia after the two-day G7 gathering, said at the weekend that the defeat of Islamic State remained the U.S. priority, while the U.S. Ambassador to the United Nations Nikki Haley said that "regime change" in Syria was also a priority for Trump.
Italy's Foreign Minister Angelino Alfano (R) gestures as he talks with US Secretary of State Rex T
The mixed messages have confused and frustrated European allies, who are eager for full US support for a political solution based on a transfer of power in Damascus.
A senior European diplomat, who declined to be named told Reuters: ”The Americans say they agree, but there's nothing to show for it behind (the scenes). They are absent from this and are navigating aimlessly in the dark."
The question of how to deal with terrorism will also be discussed when start at 2.30pm (GMT) today.
US Secretary of State Rex Tillerson speaks to the press
The foreign ministers will talk about growing tensions with North Korea, as the United States moves a navy strike group near the Korean peninsula amid concerns over Pyongyang's nuclear ambitions.
They will also discuss Libya. Italy is hoping for vocal support for a United Nations-backed government in Tripoli which has struggled to establish its authority even in the city, let alone in the rest of the violence-plagued north African country.
US Secretary of State Rex Tillerson
The Trump administration has not yet defined a clear policy and Rome fears Washington may fall into step with Egypt and Russia, which support general Khalifa Haftar, a powerful figure in eastern Libya.
Some issues, such as trade and climate change, are likely to be ducked this week. "The more complicated subjects will be left to the leaders," said an Italian diplomat, who declined to be named because he was not authorised to speak to the press.