In a shift in Washington's strategy, US missiles hit a Syrian air base last week in retaliation for what the United States and its allies say was a poison gas attack by Syria's military in which scores of civilians died. The Syrian government has denied it was behind the assault.
US President Donald Trump had previously appeared disinclined to intervene against the Syrian leader and the attack raised expectations that he might now be ready to adopt a tougher-than-expected stance with Russia, Assad's main backer.
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.
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.
"What we're trying to do is to give Rex Tillerson the clearest possible mandate from us as the West, the UK, all our allies here, to say to the Russians 'this is your choice: stick with that guy, stick with that tyrant, or work with us to find a better solution'," Johnson said after meeting Tillerson.
Russia has rejected accusations that Assad used chemical arms against his own people and has said it will not cut its ties with Assad, who has been locked in a six-year-old civil war that has devastated Syria and displaced half its population.
"Returning to pseudo-attempts to resolve the crisis by repeating mantras that Assad must step down cannot help sort things out," Dmitry Peskov, spokesman for Russian President Vladimir Putin, said on Monday.
Johnson said he was keen to seen further sanctions imposed on both Syrian and Russian "military figures". Speaking to reporters in France, Canadian Prime Minister Justin Trudeau said his country was also ready to stiffen sanctions on Moscow.
"CRIMES AGAINST INNOCENTS"
Tillerson said at the weekend the main priority for the United States was the defeat of one of Assad's main foes, the ISIS terrorist movement, and it is unclear how far he will want to push the Russians on Tuesday.
On Monday, the former oilman-turned-diplomat visited the site of a World War Two Nazi massacre in Italy and said the United States would never let such abuses go unchallenged.
As the talks began, a few dozen anti-G7 protesters clashed with baton-wielding riot police on the edges of the walled city.
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. All oppose Assad's rule.
Before the meeting started, the foreign minister of Iran, which supports Assad, asked to speak to Italian Foreign Minister Angelino Alfano to discuss Syria, Italian diplomats said. Details of their conversation were not disclosed.
The foreign ministers' discussions will prepare the way for a G7 leaders' summit in Sicily at the end of May, which looks set to be Trump's first overseas trip since becoming president.
The ministers will also talk about growing tensions with North Korea, with the United States moving a navy strike group near the Korean peninsula amid concerns over Pyongyang's nuclear ambitions.
They will also debate 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 country.
The Trump administration has not yet defined a clear policy and Rome fears Washington may fall into step with Egypt and Russia, which both support general Khalifa Haftar, a powerful figure in eastern Libya.
The struggle against terrorism, relations with Iran and instability in Ukraine are also on the agenda, with the meeting expected to finish by midday on Tuesday.
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