The US raised the stakes significantly on Monday when a senior US official said Washington has made a preliminary conclusion that Russian Federation knew in advance of Syria's chemical weapons attack last week.
Jim Mattis called Friday's strike a "measured response" to the regime's "use of chemical weapons". The diplomatic damage from the alleged chemical weapons attack and the US response might yet be contained, but this is not the way either side imagined this first, important meeting.
"We have many friends in Italy", he said at the end of his lunch with Mattarella, according to the Italian press.
United States president Donald Trump has expressed skepticism about the quality of the US's own intelligence, particularly when it comes to chemical weapons. That's according to a senior United States official.
G7 efforts to build a united front against Assad comes just ahead of Tillerson's trip to Moscow, the first for a high-ranking Trump administration official.
"Russia's allegations fit with a pattern of deflecting blame from the (Syrian) regime and attempting to undermine the credibility of its opponents", one of the officials said.
Trump discussed Syria during separate telephone calls Monday with British Prime Minister Theresa May and German Chancellor Angela Merkel.
The attack led the Trump administration to harden its attitude against Syrian President Bashar al-Assad weeks after top USA officials said they were more concerned with defeating Islamic State militants than getting Assad out of power.
Or, he added, it could maintain its alliance with Syria, Iran and militant group Hezbollah, "which we believe is not going to serve Russia's interests' longer term".
"He [Putin] must understand that Assad is now toxic in every sense".
That likelihood was backed up by White House spokesman Sean Spicer on Monday, who warned Syria against further use of chemical weapons or chlorine-laden barrel bombs. But he made explicit that the US sees no future for the Assad regime in Syria.
"It is unclear whether Russian Federation failed to take this obligation seriously and whether Russian Federation has been incompetent".
The violence in Syria has brought to a boiling point years of escalating tension with Moscow - the tension surged with the invasion of Ukraine in 2014, followed by painful economic sanctions, and then divergent views on Assad.
The U.S.is hinting that its true long-term objective in striking the airfield was to send a political message - that long-term peace in Syria will require changes in government, and the countries backing Assad should stop keeping him in place.
The Kremlin is watching the Group of Seven meeting of foreign ministers from industrialized nations in Italy for signs of a united Western front, of the "clear and coordinated message" that British Foreign Secretary Boris Johnson promised as he cancelled his own visit to Lavrov in Moscow.
Italian media said the aim was "to avert a unsafe military escalation".
Before heading to Russia, Tillerson told reporters it was unclear whether Moscow had failed to take seriously its obligation to rid Syria of chemical weapons, or whether it had merely been incompetent.
Japan hopes the strong USA response on Syria will also put pressure on Pyongyang, which is showing signs of preparing for its sixth nuclear test and more test-firings of ballistic missiles.
Tillerson's trip comes after an American official said the US has drawn a preliminary conclusion that Russian Federation knew in advance of the chemical attack - an allegation that heightens already acute tensions between Washington and Moscow.