Rex Tillerson will also meet officials from allied Middle Eastern countries before heading to Moscow.
The UK has suggested threatening tightly-focused sanctions on Russian and Syrian military officers.
The moves follow the latest apparent use of chemical weapons in Syria.
The Associated Press news agency quoted a senior US official as saying that the Russians knew of the chemical attack because a drone had been flying over a hospital in Khan Sheikhoun as victims sought help.
In response, the US says it destroyed a fifth of Syria’s operational aircraft in an air strike on the Shayrat airbase last Thursday and said further strikes could take place.
German Chancellor Angela Merkel meanwhile agreed with President Trump that President Assad should be held accountable, the White House said.
However Washington’s Syria policy remains unclear to many, with Mr Tillerson saying that there had been “no change to our military posture” in Syria following the US airbase strike and that Washington’s “first priority” was to defeat so-called Islamic State (IS).
UK Foreign Secretary Boris Johnson said sanctions could target high-ranking Syrians and Russians who had been involved in coordinating Syrian military operations.
These would be the first sanctions against Russian figures over Syria if they were to be adopted.
The BBC’s James Robbins in the Italian town of Lucca, where the G7 ministers are meeting, says British officials recognise that more general sanctions on Russia would probably be resisted by some G7 countries, including Germany and Italy.
Russia is already subject to a raft of sanctions imposed by the US and EU in response to the annexation of Crimea and the crisis in eastern Ukraine.
In a sign of the tensions between the US and Russia, the Kremlin has said that Mr Tillerson will not meet President Vladimir Putin.
Sticking to protocol, he will hold talks with his Russian counterpart, Sergei Lavrov. While he has known Mr Putin for years, Mr Tillerson will be the first US secretary of state not to meet the top Russian leader on a first trip to Moscow.
Russia says the US has failed to provide evidence that Syria has chemical weapons.
Russia and Iran, President Assad’s key military backers, are also threatening retaliation if there are any further American air strikes.