The G-7 blames Assad's military for a deadly chemical attack last week. Ministers meeting in Lucca, central Italy, have strongly supported US missile strikes that targeted a Syrian air base believed to have been used to launch the attack.
Italian Foreign Minister Angelino Alfano said the US intervention had offered "a window of opportunity to construct a new positive condition for the political process in Syria." But he said a political rather than military process was "the only solution," according to Italian news agency ANSA.
British Foreign Secretary Boris Johnson said the G-7 was considering new sanctions on Russian military figures to press Moscow to end military support for the "toxic" Assad government.
US officials in Washington have also raised that prospect. But others want a more conciliatory approach. German Foreign Minister Sigmar Gabriel said Russia, and Assad ally Iran, must be involved in any peace process to end Syria's six-year civil war.
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Gabriel said the United States had "sent a clear signal to the Assad regime" by launching cruise missiles at a Syrian air base, but said other nations should "reach out to Russia" rather than seek a military escalation.
Japanese foreign ministry spokesman Masato Ohtaka said that "in terms of dialogue and other political engagement I think a lot of countries think that Russia can play a key role."
The G-7 wants to deliver a united message to Russia through US Secretary of State Rex Tillerson, who heads to Moscow after Tuesday's meeting.
The other G-7 members Germany, France, Britain, Canada, Japan and current president Italy are also trying to grasp what the US administration's foreign policy is, amid conflicting signals from Washington.