Foreign ministers from the seven countries said Moscow can play a constructive role in ending the brutal conflict that has destabilized the Middle East, driven millions to escape Syria and further frayed relations between the West and Russian Federation. USA agencies are investigating Russia's alleged role in trying to influence last year's USA election, complicating efforts to find common ground in tackling ISIL.
The focus of the attacks was on Idlib in northern Syria, the central Hama province and southern Deraa, which are the remaining strongholds of rebels fighting to oust Assad.
There was one key difference: After the recent launch of 59 Tomahawk cruise missiles on a Syrian air base, President Donald Trump can now offer each a credible threat that the US will use force in Syria if the stalemate persists.
It wasn't clear what the punishment would be for a Russian government that has used its military might to help Assad and his array of allies score a series of battlefield successes in their six-year war with Syrian opposition groups.
US Secretary of State Rex Tillerson is due to travel to Moscow on Tuesday at the end of the two-day gathering in the Tuscan city of Lucca with his Italian, German, French, British, Japanese and Canadian counterparts.
"We can not let this happen again", the secretary of state said.
Also on Monday, Britain and Canada said sanctions could be tightened on Moscow if it continued to back Assad.
The leaders of southern European Union nations said yesterday (10 April) that a United States missile strike on a Syrian airbase in retaliation for a suspected chemical attack was "understandable", as diplomatic tensions mount over the incident.
Calling the strike a "game changer", British Foreign Secretary Boris Johnson said support for the Syrian president "was toxifying the reputation of Russia" and suggested sanctions could be imposed on Moscow if it refused to change course.
SYRIA OPPOSES: President Bashar al-Assad's office denounced the US strike as 'reckless, irresponsible behavior'.
Others argued for a more conciliatory approach.
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Mr Tillerson said it was unclear whether Russian Federation had failed to take its obligations in Syria seriously, or was incompetent, but he said the distinction "doesn't much matter to the dead".
"Not everyone may like it, but without Moscow and without Tehran there will be no solution for Syria", he said. It is the first official trip to Russian Federation by a member of President Donald Trump's Cabinet.
"These [US] strikes turned out to be useless, Assad is still intent on attacking.in some places the strikes are even worse", said one rebel fighter, who asked not to be named.
The US secretary of state said the Khan Sheikhoun attack showed Moscow had failed in its role under the terms of an earlier United Nations agreement to guarantee that Syria remained free from chemical weapons.
On Monday Tillerson raised fresh expectations for aggressive US action - and not only in Syria - as he visited the site of a World War II Nazi massacre in central Italy, saying the USA would hold to account "all who commit crimes against the innocents anywhere in the world". Yet the USA has no proof of Moscow's involvement, said the official, who wasn't authorized to speak publicly on intelligence matters and demanded anonymity.
Looking to build their case against Assad, Italy has invited the foreign ministers from Turkey, Saudi Arabia, United Arab Emirates, Jordan and Qatar to sit down with the G7 group on Tuesday to discuss Syria. His new administration has generally downplayed human rights concerns while promoting an "America First" strategy de-emphasizing the concerns of foreign nations.
The United States has sought to minimize expectations for the trip or the likelihood that the US will leave with any Russian concessions on Syria.
The G-7 members broadly agree that Assad should go - but not necessarily when, or how.
"That's why we are not presupposing how that occurs", Tillerson added.
"I think it is clear to all of us that the reign of the Assad family is coming to an end".