Lucca - President Bashar al-Assad should not be part of Syria's future, US Secretary of State Rex Tillerson said on Tuesday, as G7 allies rejected a call for new sanctions on Damascus and its key ally Moscow.Washington has stepped up the pressure on Russia to rein in Assad after a suspected chemical weapons attack on a rebel-held Syrian town that killed at least 87 civilians and triggered retaliatory US missile strikes on a Syrian air base.Direct responseAs G7 foreign ministers urged a diplomatic push to end the six-year conflict and create a lasting peace for a unified Syria, Tillerson said: "Our hope is Bashar al-Assad will not be part of that future."With a growing gulf between the US and Assad's main ally Russia, the G7 ministers threw their support behind Tillerson as he headed for vital talks on the Syrian conflict in Moscow."To be clear, our military action was a direct response to the Assad regime's barbarism," Tillerson said at the G7 meeting in Italy."The United States' priority in Syria and Iraq remains the defeat of ISIS," he added.Moscow said it was hoping to avoid confrontation and engage in "constructive cooperation" with Washington, as Tillerson headed to the Russian capital on the first visit by a senior member of President Donald Trump's administration.The G7 ministers failed to agree on whether fresh sanctions should be imposed on Damascus and Moscow.Peaceful resolution"At the moment there is no consensus on new sanctions as an effective instrument," Italy's Foreign Minister Angelino Alfano said, after his British counterpart Boris Johnson had raised the issue.But after talks in the Tuscan city German Foreign Minister Sigmar Gabriel said: "All the G7 states want to avoid a military escalation and want a political solution without a new spiral of violence."We want to bring Russia around to supporting the political process for a peaceful resolution of the Syrian conflict."