Russian officials have requested a meeting with the UK's Foreign Secretary Boris Johnson to discuss the nerve agent attack on former double-agent Sergei Skripal and his daughter Yulia.
The British Foreign Office confirmed that it had received a request from the Russian Embassy for a meeting with Mr Johnson, one of the most vocal British Government critics of Vladimir Putin's regime over the attempted assassination.
It comes as speculation mounted that the Skripals could be able to offer officers investigating the Salisbury nerve agent attack missing clues as the pair continue to recover.
An FCO spokeswoman said: "We have received a request. We will be responding in due course."
Mr Skripal, 66, and his 33-year-old daughter Yulia were left fighting for their lives in hospital after being found unconscious on a park bench in Salisbury on March 4.
The former double agent is "responding well to treatment, improving rapidly and no longer in a critical condition", Salisbury District Hospital said.
British Foreign Secretary Boris Johnson said the improvement in the condition of Mr Skripal was "great news" and "testament to the quick work" of the emergency services.
In a statement posted on its website on Saturday, the Russian Embassy said "interaction" between it and the Foreign Office was "utterly unsatisfactory".
They added: "We believe that it is high time to arrange a meeting between Ambassador Alexander Yakovenko and Foreign Secretary Boris Johnson in order to discuss the whole range of bilateral issues, as well as the investigation of the Salisbury incident.
"Ambassador Yakovenko has already sent a respective personal note to the Foreign Secretary.
"We hope that the British side will engage constructively and that such meeting is arranged shortly."
Moscow has denied being responsible for the poisoning of the Skripals but the incident has plunged diplomatic relations between Russia and the West into the deep freeze.
The Russian Embassy had previously said it hoped the improvement in the Skripals' health will "contribute to the investigation of the crime perpetrated against them".
Ms Skripal made her first public comments on Wednesday shortly after Russian TV reported that she had contacted her cousin Viktoria in Moscow to say she and her father were recovering and that she would soon be discharged.
The UK authorities have refused to grant Viktoria Skripal a visa to come to Britain, with the Home Office saying her application "did not comply with the immigration rules".