British Ambassador Tony Brenton was earlier summoned to the Foreign Ministry over the decision by the British Embassy's cultural arm to keep open its offices in Yekaterinburg in the Urals and in St. Petersburg.
"The [British] ambassador was told that Russia considers such actions to be a deliberate provocation aimed at increasing tensions in Russian-British relations," the ministry said in a statement.
Russian authorities had ordered the British Council to suspend its regional operations as of January 1 over tax and legal status violations.
A British Council official in Moscow said: "British Council activities in Yekaterinburg, St. Petersburg and Moscow fully comply with Russian and international laws, and that is why we see no reason why we should abstain from continuing operations."
Russian Foreign Ministry Spokesman Mikhail Kamynin said in a statement that the Council's regional offices violated the 1963 Vienna convention on consulate relations.
A British Embassy spokesperson said earlier that London would continue discussing the situation with Russian authorities to find a solution as soon as possible, so that the British Council can resume its activities.
Konstantin Kosachyov, who heads the international affairs committee in the lower house of Russia's parliament, reiterated on Monday that Russia's claims against the British Council lacked a political motivation, and were of a legal and financial nature.
The British Council, non-profit organization that promotes education and cultural programs, first established an office in Moscow in the 1990s and went on to open a further 14 offices across Russia.
The organization has been involved in three years of legal wrangling with Russian authorities over the alleged non-payment of tax and issues relating to its legal status.
