RT said on Monday that NatWest, owned by Royal Bank of Scotland Group (RBS), was withdrawing its banking services from the channel's British arm. RT and Russian diplomats accused the bank of attacking freedom of speech.
Maria Zakharova, the Foreign Ministry's spokeswoman, told reporters on Tuesday that Moscow would retaliate in kind if necessary. That prompted speculation a British media organisation operating in Russia could encounter problems.
Zakharova wrote on Friday in a post on social media that the scandal was starting to "reek of" the BBC, pointing out that the corporation's Russian service had run what she dismissed as an empty investigation into RT's UK activities.
"Why did they do this?" she wrote. "So that a nasty taste stayed behind."
"I wish the BBC Russian service luck. They will need it now, because digging stuff up can be a diverting and unpredictable business."
Three pro-Kremlin senators in the upper house of parliament have already urged Russian authorities to hit back by closing the BBC's bank accounts in Russia, the RIA news agency reported on Monday.
RBS, which is owned by the British state, has said it is reviewing the situation and will contact RT to discuss the matter further.
(Reporting by Andrew Osborn; Editing by Christian Lowe)