Renewed international focus Syria follows an American air strike ordered by Donald Trump, which saw 59 Tomahawk missiles hit the al-Shayrat air base near the city of Homs.
The attack was authorised after 87 people, including children, were killed in a suspected sarin nerve agent strike on Khan Sheikhoun.
Speaking outside the summit, Mr Johnson said: The United States have already imposed some extra sanctions themselves, and we will be discussing the possibility of further sanctions certainly on some of the Syrian military figures and indeed on some of the Russian military figures who have been involved in coordinating the Syrian military efforts and of course who are thereby contaminated by the appalling behaviour of the Assad regime.
He added: “It is the Americans who have changed the game by using those cruise missiles which never happened in the last five years, so the game has now been changed and I think it’s important that that message should be heard from the Americans to the Russians.”
Asked why he believed sanctions would now work , he told reporters: “I think the Russians need a way out and a way forward and if I think about the position of Vladimir Putin now he is toxifying the reputation of Russia by his continual association with a guy who has flagrantly poisoned his own people, and I think the world can see this.
“The evidence by the way is overwhelming, he should look at the evidence for what happened the other day.
“It is absolutely conclusive, so what we’re trying to do is to give Rex Tillerson the clearest possible mandate from us as the West, the UK, all our allies here to say to the Russians this is your choice: stick with that guy, stick with that tyrant or work with us to find a better solution.”
Discussing America’s response to the attack, something described by Assad’s allies as having crossed a “red line”, Mr Johnson suggested that the US could launch fresh strikes in the fight to weaken President Bashar Assad’s regime.
He told The Sun: “Crucially – they could do so again.
“We cannot miss this moment. It is time for (Russian president Vladimir) Putin to face the truth about the tyrant he is still propping up.”
Theresa May spoke to Justin Trudeau, the Canadian Prime Minister, on Sunday night and said that Russia must help secure a “political settlement” in Syria.
A Downing Street spokesman said: “They spoke to discuss events in Syria following the chemical weapons attacks. They agreed on their support for the US action, that it was an appropriate response to the barbaric chemical weapons attack launched by the Syria regime.
“They discussed the importance of Russia using its influence to bring about a political settlement in Syria and to work with the international community to ensure that the shocking events of last week are never repeated.
“They noted the Foreign Secretary is working closely with his Canadian counterpart.”
The possibility of an attack came after the Russian embassy in the UK suggested that British and American attempts to deliver an ultimatum to the Kremlin this week could result in a “real war”.
Both Russia and Iran have threatened military retaliation against the US, accusing Mr Trump of crossing “red lines” by ordering a cruise missile attack on a Syrian air base.
The two military allies of Syria said the US bombardment had violated international law and, in a statement, added: “From now on we will respond with force.”
Mr Johnson is understood to be working on a proposal from the G7 group of nations which will demand that Mr Putin withdraws his support of Assad.
Mr Johnson cancelled plans to visit Moscow this week to work on the proposal – which The Daily Telegraph understands will include a tacit offer to Russia to rejoin the G7 if it complies.
On Sunday Russia mocked Mr Johnson, saying his refusal to visit was “deplorable” and, in a series of jibes on Twitter, questioned whether he would make a fit wartime lieutenant to the American president.
Sir Michael Fallon, the Defence Secretary, warned Russia it is responsible for the deaths caused by the Syrian chemical weapons attack “by proxy”.
Rex Tillerson, US secretary of state, echoed the comments, telling Face The Nation on CBS, the Russians “have played now for some time the role of providing cover for Bashar Assad’s behaviour”.
He also said on Monday that America was ready to take action to defend innocent people.
“We want to be with those who know how to respond to those hurting innocent people in any part of the world,” he said at a memorial for the 560 victims of a Nazi World War II massacre in the Tuscan town of Sant’Anna di Stazzema.
“This place will be an inspiration for our action.”
Former head of MI6 Sir John Sawers supported the intervention in Syria but expressed serious concerns about Mr Trump’s ability to manage the complex diplomatic challenges in the Middle East and North Korea.
He told BBC Radio 4’s Today programme:”Whilst the tensions this morning and this week around the world are higher, the enforcement of international norms actually is in the long-term interests of the West and the world generally, to rule out the use of chemical weapons in any circumstances.”
Asked if he was scared of Mr Trump, the former diplomat and spymaster said: “He is not someone who fills me with confidence.
He doesn’t have the background and the experience and the instincts of being an effective US president.
“But it is in our interests that we have a US administration which upholds the international system, that supports its allies and supports international norms.” He said the last week had shown “sensible grown-ups within the administration taking charge and the rather ideological figures around Trump himself being marginalised”.