Russia's foreign ministry has said the country's relations with the US are the most difficult since the end of the Cold War.
It comes ahead of a visit by US Secretary of State Rex Tillerson to Moscow - and after G7 foreign ministers rejected UK Foreign Secretary Boris Johnson's calls to broaden sanctions against Russia and Syria.
Pressure has been mounting on Russia to end its support for Syrian leader Bashar al Assad following the US missile attack on a Syrian airbase, carried out in retaliation for a chemical weapons attack blamed on the president's regime - something it denies.
However, at a news conference at the close of the summit, Italian foreign minister Angelino Alfano said Russia must not be "pushed into a corner" over Syria.
Mr Tillerson, who is heading to Moscow to work on "a solution which will deliver a lasting political settlement" in Syria, has raised fresh expectations of aggressive military action against the country and any other repressive regimes .
Speaking in a tougher tone than his Italian counterpart, he said Russia had a choice - to align itself with the US and like-minded nations, or with Mr Assad, Iran and the militant group Hezbollah.
Mr Tillerson said it was unclear whether Russia had failed to take its obligations in Syria seriously, or whether it was was incompetent, but he said the distinction "doesn't much matter to the dead".
He said another chemical weapons attack could not be allowed to happen, adding: "It is clear to us the reign of the Assad family is coming to an end."
Mr Johnson had seen the G7 summit as a game-changing moment and had called for new sanctions to be imposed on Syrian military figures and Russian military individuals responsible for backing them.
But the question of added sanctions had barely been mentioned in the meetings, according to French foreign minister Jean-Marc Ayrault.
The outcome has fallen well short of that, with the countries agreeing there could be no Syrian peace deal with Mr Assad in power.
However, it was unclear how the group of seven nations expected Mr Assad's departure to be brought about.
Sky's Political Correspondent Tamara Cohen, who was in Lucca, Italy, for the G7 summit, said: "Interestingly, sanctions didn't feature in Theresa May's phone call with Donald Trump last night, but they did believe this was a window of opportunity to put pressure on Russia."
Mr Johnson insisted afterwards his proposals "had a wide degree of acceptance... but you've got to do these things in the proper, legal way".
He told Sky News: "What I think we all want to see is Russia engaging with a political process that involves a transition to a new government in Syria.
"I think that's the offer that Rex Tillerson is going to be making, and I think it's a powerful one, but you must be realistic that we've been here before."
He continued: "Did they know that Assad was going to unleash chemical weapons? We have no evidence for that.
"It may very well be that they've simply been betrayed by their client, by they guy they've been backing.
"Now is the time for them to recognise that and help the rest of the world, and above all help the people of Syria, to move forward."
:: The dangers of playing Russian roulette in Syria
The US has concluded that Russia knew in advance of Syria's chemical weapons attacks and then attempted to cover it up by bombing a hospital where victims had been taken, a senior official said.
But another official said it was too early for clear-cut conclusions to be reached.
Russian president Vladimir Putin and his Iranian counterpart, Hassan Rouhani, have warned the US that airstrikes on Syria crossed "red lines" - echoing Mr Trump's condemnation of the gas attack itself.
Sky's Foreign Affairs Editor Sam Kiley, in Moscow, said: "At the moment Russia holds all the cards when it comes to the future of the Assad regime.
"It is very much in Russia's gift, alongside Iran of course which is a very significant player, to put pressure on the Assad regime to participate in a transition out of power if it so chose to go down that route.
"Given that they are militarily very much with the upper hand on the ground in Syria against the Syrian rebels, I don't think they're minded to take that route at all in Moscow, not least at a time when they are being talked at from their perspective, lectured by the international community on what should go on in Syria.
"I think that the message they will want to deliver is 'we want some respect in this context'."