Foreign ministers were seeking a common position on the Syrian conflict, before the U.S. secretary of state flies to Russia to try to persuade it to abandon its Syrian ally, the BBC reported.
The nations agreed there was no solution to the Syria crisis with President Assad in power.
But UK proposals to target sanctions at senior military leaders were sidelined.
Read alsoTrump sending important signal for both Ukraine, Putin – Russian expertThe diplomacy in the Italian town of Lucca follows the latest apparent use of chemical weapons in Syria.
Syria has denied it carried out a chemical attack on the rebel-held town of Khan Sheikhoun last week that left 89 people dead.
In response, the U.S. fired 59 cruise missiles at a Syrian airbase that it said was implicated in the attack.
Speaking after the end of the G7 meeting, U.S. Secretary of State Rex Tillerson said the missile strike "was necessary as a matter of US national security interest".
"We do not want the regime's uncontrolled stockpile of chemical weapons to fall into the hands of Isis or other terrorist groups who could and want to attack the United States or our allies.
Read alsoRussia knew of upcoming Syrian chemical attack – media"Nor can we accept the normalization of the use of chemical weapons by other actors or countries in Syria, or elsewhere."
Mr. Tillerson will head to Moscow for talks on Syria later on Tuesday, hoping to persuade the Russians that they have an unreliable ally in President Assad.