During his first day in Italy, Tillerson plans to meet Monday with foreign ministers from the United Kingdom and France before the G-7 summit formally opens.
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.
The U.S. received broad support from Europe after the airstrikes.
At a meeting of G7 foreign ministers in Lucca, Italy, Mr Johnson issued a fresh appeal to Russian President Vladimir Putin to abandon his backing for his Syrian ally following last week's chemical weapons attack. "I welcome this renewed harmony".
Kremlin spokesman Dmitry Peskov told reporters on Wednesday that "if it is decided" that the Russian president needs to be briefed on the outcome of the Tillerson-Lavrov talks, he will meet them.
Before leaving for Russia, Tillerson issued a stern warning to the Kremlin - either stand with the USA and other "like-minded" nations against Syria or side with Assad and his allies Iran and the militant group Hezbollah.
"Russia's initiative in 2013 to dismantle Syria's chemical weapons has been exposed as a shambles".
From Italy, Tillerson will travel to Moscow, becoming the first Trump administration official to visit Russian Federation.
Tillerson is traveling Tuesday to Moscow.
UP govt to take views of Muslim women on triple talaq issue
The submissions drawn by advocate Madhvi Divan have been settled by the Attornewy Genewral Mukul Rohatgi. A number of Muslim women have filed petitions to quash the practice of triple talaq and polygamy.
The missile attack was in response to Syrian military forces using chemical weapons to attack Syrian civilians.
Tillerson says it's unclear whether Russian Federation failed to take seriously its obligations in Syria or has been incompetent.
Russia's veto of a United Nations resolution condemning a deadly chemical attack in Syria and pushing Bashar Assad's regime to co-operate with an worldwide inquiry put the country on the "wrong side" of the argument, Boris Johnson has said.
But on Monday, U.S. Secretary of State Rex Tillerson visited the site of a World War Two Nazi massacre in Italy and said Washington would never let such abuses go unchallenged.
This frame grab from video provided on Tuesday April 4, 2017 shows a Syrian doctor treating a boy following a suspected chemical attack, in the town of Khan Sheikhoun, northern Idlib province, Syria.
"The United Kingdom therefore shares the U.S. assessment that it is highly likely that the regime was responsible for a sarin attack on Khan Sheikhoun on April 4", Mr Rycroft said.
Tillerson's Moscow talks hinge on new U.S. leverage over Syria.
Trump used the same argument in December, when the intelligence community issued its official assessment that Russian Federation interfered with the US election.
Earlier, the United States military's Central Command spokesman Colonel John Thomas said the USA strike at Shayrat airfield near Homs in central Syria had destroyed more than 20 Syrian jets. He says that makes it hard to have clarity about USA positions.