Protesting outside the Russian embassy over Syria would increase the "hysteria and jingoism" that is being "whipped up" against the federation, peace campaigners have claimed.
The Stop the War Coalition claimed the Government is fuelling anti-Russian sentiment in an attempt to "justify" an escalation of British military intervention.
Foreign Secretary Boris Johnson called directly on the campaign group on Tuesday to stage embassy protests over the continued attacks by Russian warplanes on the stricken city of Aleppo.
But Stop the War vice chairman Chris Nineham said the organisation would not stage any demonstrations.
"The reason for that is our focus is on what our Government is doing," he told the BBC Radio 4 Today programme.
"There's a very good reason for this, because we can make a difference to what Britain does, we can make a difference to what our allies do to a certain extent and we have done.
"But, if we have a protest outside the Russian embassy it wouldn't make a blind bit of difference as to what (President Vladimir) Putin does because we are in Britain and were are in the West.
"And, not only that - a protest outside the Russian embassy would actually contribute to increasing the hysteria and the jingoism that is being whipped up at the moment against Russia."
He added: "What we are saying is there is a hysteria which is being organised by politicians and the media against Russia to see Russia as the only problem in Syria."
Mr Nineham said the Foreign Secretary's calls for demonstrations were "characteristically trivialising".
In an emergency Commons debate, Mr Johnson said Russian President Vladimir Putin was in danger of turning his country into an ''international pariah'' with his continued support for the regime of President Bashar Assad.
''It is the UK week after week that is taking the lead together with our allies in America and in France, all the like-minded nations, in highlighting what is happening in Syria to a world where, I'm afraid, the wells of outrage are growing exhausted,'' he said.
''There is no commensurate horror, it seems to me, amongst some of those anti-war protest groups. I'd certainly like to see demonstrations outside the Russian embassy. Where is the Stop the War Coalition at the moment? Where are they?''
Mr Johnson has previously angered Russia by claiming that its forces may have been guilty of war crimes last month when air strikes hit a UN aid convoy near Aleppo, finally ending a fragile ceasefire.