It is clear "to all of us that the reign of the Assad family is coming to an end," US Secretary of State Rex Tillerson has said.

The United States "hopes" for a Syria without Bashar al-Assad in charge, he added at a summit in Lucca, Italy.

It came as Britain and America failed to win immediate support from European allies for new sanctions on Russia following the chemical weapons attack in Syria.

Foreign Secretary Boris Johnson had lead the effort to impose sanctions over Russia's support for the Assad regime.

Mr Tillerson said: "The question of how [Mr Assad's rule] ends and the transition itself could be very important in our view to the durability, the stability inside of a unified Syria.

"That's why we are not presupposing how that occurs."

"We want to relieve the suffering of the Syrian people. Russia can be a part of that future and play an important role," Mr Tillerson added in remarks to reporters. "Or Russia can maintain its alliance with this group, which we believe is not going to serve Russia's interests longer term."

Russia's foreign ministry said in a statement that it hoped for "productive talks" when the top US diplomat visits Moscow. It said the outcome of the discussions is important not only for the Russia-US relationship, but "for the overall atmosphere on the world stage".

On Monday night US Defence Secretary James Mattis warned the Syrian government it would be "ill-advised ever again to use chemical weapons", and US officials said they had concluded Russia knew about the attack, on the village of Khan Sheikhoun, in advance.

Gen Mattis' strong rhetoric followed two days after Russia and Iran told the US they would "respond with force" if their own "red lines" were crossed in Syria.