Moscow: State-funded Russian broadcaster RT complained on Monday that NatWest had withdrawn its banking services in Britain without explanation, questioning how the move squared with the right to freedom of speech.
The bank later clarified that the services remained in place and its decision to rescind them was being reviewed.
RT published NatWest's letter on its web site, saying that the bank, which is part of the Royal Bank of Scotland Group, had reached the decision after "careful consideration" and that the determination was final.
NatWest said in the letter it was not prepared to discuss the matter further.
The move is likely to make it harder for RT, which often features guests who criticise the West while presenting the Kremlin's point of view, to operate in Britain.
Margarita Simonyan, editor-in-chief of RT, reacted sarcastically on social media, writing "Long live freedom of speech!", while Russian Foreign Ministry spokeswoman Maria Zakharova said it looked like Britain had abandoned its commitment to freedom of speech.
Simonyan said she did not know what was behind the decision, but told the RBK news portal that one theory was that it was part of a new British sanctions package against Russia.
In the letter to RT it had said the decision was final and it was "not prepared to enter into any discussion".
On Monday evening, however, after a day of being criticised for taking a political, anti-free speech decision, NatWest backed down.
A spokeswoman for NatWest's parent bank RBS said "These decisions are not taken lightly. We are reviewing the situation and are contacting the customer to discuss this further. The bank accounts remain open and are still operative."
An RBS spokeswoman told Fairfax the bank would give "no details" on the reasons for the accounts being closed.
Asked if the latest statement meant the bank had stepped back from its earlier statement that the decision was final, she said "I think you could come to that conclusion".
RT has been a NatWest customer for more than 10 years.
The spokeswoman said the broadcaster was concerned this would not be confined to one bank but would be "reflected in wider banking issues for RT".
RT's Moscow press office told Fairfax Media: "This decision is incomprehensible, and without warning.
"It is however, not at odds with the countless measures that have been undertaken in the UK and Europe over the last few years to ostracize, shout down, or downright impede the work of RT."
"RT UK will continue its operations uninterrupted."
Commentators on the channel speculated the bank had made a political, rather than a business decision.
Relations between Moscow and London are strained by differences over Syria and Ukraine, and British Foreign Secretary Boris Johnson last week angered Russia with a call for people to protest outside the Russian embassy over Russia's air strikes on the Syrian city of Aleppo.
British broadcast regulator Ofcom has ruled against RT in the past over what it said were a series of biased or misleading programmes on Syria and Ukraine. It said the content flouted Britain's broadcasting code.
The Russian government accused Barclays of censorship last year after the British bank accounts of state news agency Rossiya Segodnya were shut. The agency's head, Dmitry Kiselyov, is on an EU sanctions list related to Russia's actions in Ukraine.
Reuters, with Nick Miller