The US secretary of state has said he hopes Russia will abandon its support for Syrian President Bashar al-Assad because actions such as last week's chemical attack have stripped him of all legitimacy.

Rex Tillerson made the remarks at the conclusion on Tuesday in Italy of a meeting of foreign ministers of the Group of Seven (G7) and "like-minded" countries.

"It is clear to us the reign of the Assad family is coming to an end," he said shortly before leaving the Tuscan city of Lucca for Moscow.

"We hope that the Russian government concludes that they have aligned themselves with an unreliable partner in Bashar al-Assad."

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A British proposal to slap extra sanctions on Syrian and Russian military officials, however, failed to win the support of the G7, Angelino Alfano, Italy's foreign minister, said.

Alfano, who chaired Tuesday's talks, said: "At this time there is no consensus for further new sanctions as an effective tool for reaching the objective that we have set ourselves."

He also said that Russia should not be "pushed into a corner" over Syria, but that it should put pressure on Assad to stop the use of chemical weapons, and should join the international push for peace in Syria.

The Syrian government has denied it was behind the April 4 attack in the town of Khan Sheikhoun.

Russia has also rejected the accusations that Assad used chemical arms against his own people while stating that it will not cut its ties with him.

Assad 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, spokesperson for Russian President Vladimir Putin, said on Monday.

The same day, Boris Johnson, the UK's foreign minister, praised last week's US missile strike on a Syrian airbase as a "game changer". He said that support for Assad "was toxifying the reputation of Russia" and suggested that sanctions could be imposed on Russia if it refused to change course.

However, Lina Khatib, head of the Middle East and North Africa programme at Chatham House, says it is questionable whether sanctions would have any effect on Syria.

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"We know that sanctions alone will not make much of a difference," she said, speaking to Al Jazeera from London on Tuesday.

"We have seen sanctions against Ukraine, and they didn't achieve much. So, the only way forward is a dialogue with Russia.

"Rex Tillerson's visit to Russia is not going to be a game changer. It is a start but we know that after this visit, Russia is not going to declare it has severed its ties with the Assad regime. What will make a difference is if Russia sees that there is the political will on part of the United States."

Khatib said if the US took this opportunity to show that regime change or political transition was a serious priority and that the administration was willing to engage in political action in order to make it happen, it would cause Western countries to rally behind the US.

"This will be what will bring Russia to the negotiating table as [the Russians] have so far only paid lip service to political change," she said.