Friday's match in Podgorica got off to a controversial start as Russia goalkeeper Igor Akinfeev was struck by a flare thrown from the stands almost immediately after kick-off, prompting a lengthy suspension in play.
The game resumed after a delay of more than half an hour, with Akinfeev taken to hospital, only for further problems to arise.
After Roman Shirokov had seen a 66th-minute penalty for Russia saved, Dmitri Kombarov appeared to be hit by another object thrown from the stands, sparking scuffles on and off the pitch and the eventual abandonment of the match.
RFU president Nikolai Tolstoy is quoted by his organisation's official website as saying: "We can only regret that the ugly behaviour of fans marred ... a very interesting and important football match between Montenegro and Russia.
"After the meeting, the RFU file an official protest to UEFA. This is what we warned [the] UEFA delegate and UEFA itself immediately after the occurrence of the incident in the first minute of the match.
"The decision to continue the game after this episode was made by the delegate after consultations. The Russian team was forced to continue the match, but I want to emphasise that we warned delegates and UEFA to file a protest.
"In our view, this [match] should be forfeited [by the] team of Montenegro."
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