"After such provocative, groundless insinuations about Moscow's aggressive policy against Kiev, cyberattacks ... the atmosphere of a possible dialogue is largely spoiled," the service said in a statement.
"From the head of the world's most authoritative intelligence service, such as MI6, we have the right to count on greater professionalism, an objective and dispassionate approach to assessing and presenting the British position on regional and international problems," the statement read.
Earlier this week, Moore said that London sees serious threats emanating from Russia and will make every effort to contain and repel all the threats posed by Moscow.
Moscow has repeatedly noted that Russia does not threaten any country and does not plan any attacks, calling such allegations groundless.