The Government is considering a request from Russia to visit Yulia Skripal in hospital, the Foreign Office said.
Ms Skripal spent three weeks in a critical condition after she and her father Sergei Skripal were exposed to Novichok in Salisbury on March 4.
The Russian Embassy said on Friday it "insists" on the right to see Ms Skripal, 33, after it emerged she was improving rapidly.
An FCO spokeswoman said: "We are considering requests for consular access in line with our obligations under international and domestic law, including the rights and wishes of Yulia Skripal."
Ms Skripal's father remains in a critical but stable condition in hospital.
The Russian embassy also accused British authorities of "another blatant provocation" after an Aeroflot flight was allegedly searched by Border Force officers at Heathrow.
An embassy official suggested that the jet, which had arrived from Moscow on a scheduled return trip, had been searched in connection with the diplomatic crisis over the Salisbury spy poisoning.
On Friday the Kremlin ordered Britain to reduce the number of diplomats in Moscow down to the same amount that Russia has in London.
It came as ambassadors from more than 20 countries were called into the foreign ministry in Moscow to be told of the latest wave of retaliatory measures being imposed.
The UK expelled 23 Russian diplomats in the wake of the poisoning of Mr Skripal, 66, and his daughter Yulia with the nerve agent Novichok.
Laurie Bristow, the UK ambassador in Moscow, was among those called into the foreign ministry in Moscow on Friday.
He told reporters: "It is important to bear in mind why this crisis has arisen in the first place.
"It's the use of a chemical weapon on the streets of the United Kingdom that has threatened the lives of a number of people in my country.
"We asked certain questions of the Russian state and have still not received adequate answers."
Russia has told a number of countries - including Ireland, Germany, Italy, France, Spain, Finland, Poland, the Czech Republic, the Netherlands, Norway and Australia - they must send home the same number of diplomats as they had ordered to leave their nations.
So far, more than 150 Russian diplomats, some of whom are suspected spies, have been told to return home by the UK's allies.
On Friday afternoon, the Russian Embassy published a list of 27 questions it claimed it had for the British authorities over the treatment of the Skripals.
The list included demands to know the exact nature of their condition and how they were being treated, and whether British doctors' approach "helped or harmed" the Skripals.
Russian Spy Sergei Skripal: Salisbury Nerve Agent Incident
Scotland Yard believes Mr Skripal and his daughter, who was visiting him from Russia, first came into contact with the deadly chemical at his home.
Detailed forensic testing revealed the highest concentration of Novichok was found on the front door.
The vast attempted murder investigation continues to unfold in the Wiltshire city, most recently leading police to cordon off a children's play area at Montgomery Gardens.
Detectives said traces of the nerve agent had been found at some of the other scenes where investigations had been carried out, but at lower concentrations.
Efforts will now focus in and around the address, and specialist teams will step back from some of the other areas investigated over the past few weeks.
Mr Skripal and his daughter have been patients at Salisbury District Hospital since they were discovered unconscious on a park bench close to The Maltings shopping centre nearly four weeks ago.
Wiltshire Police Detective Sergeant Nick Bailey, who was also exposed to the nerve agent, was discharged from the hospital last week.
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