G7 nations have failed to agree on a proposal by Britain for sanctions against Russia in the wake of a deadly chemical attack they say was carried out by Moscow's ally, Syria.
Italy's foreign minister said the group did not want to back Russia into a corner and preferred dialogue.
US Secretary of State Rex Tillerson has moved on from the G7 meeting in Italy and has arrived in Moscow for talks.
He insisted Syria's president could not play a part in the country's future.
The G7 meeting in the Italian city of Lucca followed last week's chemical attack on the rebel-held Syrian town of Khan Sheikhoun that left 89 people dead.
The Turkish health ministry on Tuesday confirmed that the nerve agent, sarin, had been used.
Syria denied the attack but the US then carried out a retaliatory strike, firing 59 cruise missiles at a Syrian airbase.
What happened at the G7?
The two-day meeting of foreign ministers was aimed at hammering out a unified approach to Syria before Mr Tillerson headed to Moscow.
But divisions arose as UK Foreign Secretary Boris Johnson proposed sanctions against Syrian and Russian military figures over the chemical attack.
BBC diplomatic correspondent James Robbins says Mr Johnson had hoped for some form of explicit support, but the final G7 communique does not mention sanctions.
Italian Foreign Minister Angelino Alfano said ministers wanted to engage with Russia.
"We think the Russians have the leverage that is needed to put pressure on [President Bashar al-Assad] and to get him to observe the commitments with regard to the ceasefire," he said.
Mr Johnson denied he had suffered a defeat, saying there was support for sanctions if further evidence of the chemical attack were gathered.
One thing that did appear to unite the group was the future of Mr Assad.
Mr Tillerson summed it up, saying: "It is clear to all of us that the reign of the Assad family is coming to an end."
He also won support over the retaliatory strike, which he called "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 [so-called Islamic State] or other terrorist groups who could and want to attack the United States or our allies," he said.
The UK's ambassador to the UN, Matthew Rycroft, later said he was circulating a new draft UN resolution, jointly with France and the US, demanding an investigation into the chemical attack that required "full co-operation".
What will Mr Tillerson face in Moscow?
Mr Tillerson will meet Russian counterpart Sergei Lavrov on Wednesday but it is unclear whether he will hold talks with President Vladimir Putin.
There were some conciliatory messages ahead of his arrival, with Moscow hoping for "constructive co-operation" with Washington.
Mr Putin hinted at this himself, saying that although Russia and Syria were being portrayed as the "common enemy" of the West, "we are ready to tolerate this", and he added: "We hope that this will nonetheless lead to some kind of positive co-operation trend."
He also called for the UN to hold an independent investigation into the chemical attack.
Reports on Monday had 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. Any such assertion on this trip is likely to strain ties further.
The BBC's Steve Rosenberg in Moscow says experience shows that Russia does not take well to threats or ultimatums.
If Mr Tillerson thinks he can weaken Moscow's support for President Assad, he may need to re-think, our correspondent says, adding that the Syrian president is Russia's key military ally in the Middle East.
A taste of this came with Mr Putin's comment on Tuesday that he had heard that "fake chemical attacks" were being prepared.
He said: "We have information from various sources that such provocations - I cannot call them otherwise - are being prepared in other regions of Syria, including in the southern outskirts of Damascus, where they are again planning to throw some kind of substance and accuse Syrian official authorities of using it."
A White House official, quoted by Reuters on Tuesday, said the US was confident that the Khan Sheikhoun attack was not carried out by rebels or "terrorists" and added that Russia had shown a clear pattern of trying to shift blame from the Syrian government.
Mr Putin said the Western response to Khan Sheikhoun reminded him of 2003, "when US envoys to the UN Security Council were demonstrating what they said were chemical weapons found in Iraq. We have seen it all already".
He also said he had heard that the US was planning more missile strikes. He gave no further information.
Russia also announced that the Syrian and Iranian foreign ministers would be in Moscow later in the week for talks.