The Russian Embassy has responded to Boris Johnson's call for demonstrations by asking if this was a "new form of British diplomacy?"
The foreign secretary said he wants to see "demonstrations outside the Russian embassy" over Moscow's role in the Syrian conflict.
The Russian Embassy earlier replied questioning what Britain had achieved in Syria so far.
Foreign Secretary Boris Johnson has called for International Criminal Court (ICC) procedures against any war crimes - such as airstrikes against hospitals and aid workers - in Syria.
Mr Johnson told MPs that "there could be advantage in ICC procedures".
In a warning to those responsible, he said: "I would remind this House that in recent history war criminals have been successfully prosecuted decades after their offences.
"Those who are conducting this bombing and in my view culpable of these crimes should realise that the mills of justice grind slowly but they grind small."
"The only realistic solution" to the Syrian conflict is a ceasefire followed by a political solution, Mr Johnson added.
After Foreign Secretary Boris Johnson and Labour's Ann Clwyd called for demonstrations outside Russian embassies over its involvement in the Syrian civil war, the Russian Embassy in the UK tweeted asking what Britain had "achieved so far?".
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Foreign Secretary Boris Johnson has said he wants to see "demonstrations outside the Russian embassy" over Moscow's role in the Syrian conflict, he told the Commons.
Mr Johnson's call came after Labour's Ann Clwyd urged those who care about the plight of Syrian civilians to gather outside Russian embassies across the globe until the country stops its bombing campaign.
The Cynon Valley MP who served as special envoy on human rights in Iraq from 2003 until 2010, said worldwide protests would make it "crystal clear" to Russia and the regime of president Bashar Assad that "we think their actions are deplorable".
Mr Johnson also warned that the "wells of outrage are growing exhausted" as the city of Aleppo faces destruction.
While Mr Johnson said the UK must take its share of refugees, the "overwhelming priority must be to help those nearest the centres of conflict and to keep them as near to their communities as we can".
The MP for Uxbridge and South Ruislip added that Russia must "do the right thing" and work towards a ceasefire in Syria.
Foreign Secretary Boris Johnson has said that all available evidence suggests that Russia was behind the airstrike on an aid convoy in Syria in September.
The attack near Aleppo left 20 aid workers and one civilian dead as they attempted to deliver aid to 78,000 civilians in the besieged city.
The former London mayor added that if Russia continues on its current path it is in danger of becoming a pariah nation.
The MP for Uxbridge and South Ruislip continued that the UK must increase its pressure on Syrian President Bashar al-Assad and Russian President Vladimir Putin by imposing sanctions on them.
Russian President Vladimir Putin "stuck two fingers up" to the UN and the international community over the bombing of an aid convoy near Aleppo in September, an MP has said.
John Woodcock, the MP for Barrow and Furness, condemned the "gortesque war crime" which left 20 aid workers and one civilian dead as they attempted to deliver aid to 78,000 civilians in the besieged city.
Saying that the attack happened shortly after a Russian drone disappeared, Mr Woodcock argued that there was "no doubt as to who were the perpetrators of this grotesque war crime.
"It was President Putin of Russia and he was sticking two fingers up to the United Nations, to the international community which he still has the audacity to claim he is a working part."
"President Putin is a classic bully", Mr Woodcock said, adding that bullies must be stood up to.
Mr Woodcock also argued that no bombing zones must be imposed in Syria and that if airstrikes occurred in these they should be met by targeting the Syrian government's forces.
Former cabinet minister Stephen Crabb has labelled the bombings in Aleppo as a "war against children".
Speaking at an emergency debate into the humanitarian crisis in the country, the Pembrokeshire MP said: "Almost half of the casualties since the current attacks began have been children, as bombs and mortars have landed on hospitals and broken through underground bunkers which sometimes also serve as schools.
"The images that we should hold before us are the ones we've seen over the last fortnight of the lifeless, dusty, broken-limbed bodies of children being removed from bombed out buildings and piles of rubble."
Former International Development Secretary Andrew Mitchell has told the Commons there are six prominent failings that have resulted in the Syrian humanitarian crisis.
- At an early stage there was a plan put forward by the former UN Secretary General Kofi Annan, who proposed that Assad should be part of the solution to the crisis. But his plan was vetoed by the US and British government, something Mr Mitchell says we now understand the importance of.
- He criticised the failure by US President Obama to stand by "the red lines" he clearly asserted on the use of chemical weapons, "a disastrous decision and one from which we will suffer in the future".
- The failure to provide safe havens for five million Syrian who have been driven out of their homes, "those safe havens could have with political will, have been set up in Idlib in the north of Syria, and across from the Jordanian border in the south."
- No-fly zones, the Tory MP criticised the fact they have not been set up. "The reality is this is a country with 22 million people and nearly half of them are on the move". Mr Mitchell questioned however if "the international community has the political will to face-down the Russians and the Syrian helicopters".
- The failure to set up access for the UN, "unprecedented in recent years, that those who are bent solely on looking after their fellow citizens should be unable to have unfettered access into very dangerous zones."
- Failure of support for the surrounding countries, in particular Jordan, Lebanon and Turkey "who have acted heroically for the extraordinary number of people who have fled often under gunfire across the borders" Mr Mitchell added that Europe has failed the refugees who have "cast themselves into the modern day slave trade in the hope of reaching a safer shore."
Shadow Foreign Secretary Emily Thornberry has rejected the suggestion that military action could be the solution to the Syrian civil war.
Ms Thornberry told an emergency debate into the humanitarian crisis in Aleppo that she is "not a pacifist" and believes in using military force "where military force can be effective", but added: "Personally I believe that in a multi-playered, mult-faceted civil war such as Syria, the last thing we need is more parties bombing.
"What we need is a ceasefire and in fact for people to draw back."
Former International Development Secretary Andrew Mitchell has accused Russia of "behaving like a rogue elephant" in Syria's civil war.
Speaking at an emergency debate in the Commons into the humanitarian crisis in the country, he said Russia were "shredding international humanitarian law" and "abusing its veto powers" on the UN security council.
The Tory MP also accused the country of using the veto to "protect itself from its own war crimes" and "doing to Aleppo precisely what the Nazis did to Guernica in the south Spanish civil war".