The threat came hours after it was revealed Yulia Skripal has been discharged from hospital, five weeks after she and her father, Sergei Skripal, were found slumped on a bench in central Salisbury on 4 March after they were poisoned.
Having made a rapid recovery in recent days, Ms Skripal was discharged on Monday and taken to a secure location.
The Russian Embassy in London said that if the Skripals were resettled in the USA, Australia, Canada or New Zealand and offered new identities – as reported – it would be “another gross violation of international law”.
A statement said: “With a secret resettlement of Mr and Ms Skripal all opportunities to hear their version of the events of 4 March will highly likely be lost forever.
“The world, while having no opportunity to interact with them, will have every reason to see this as an abduction of the two Russian nationals or at least as their isolation.”
Christine Blanshard, deputy chief executive and medical director at Salisbury District Hospital, said both Ms Skripal, 33, and her father, 66, have been responding well to treatment in the five weeks they have been in hospital.
She said they have received “round-the-clock” care and revealed that nerve agents cause hallucinations and sickness.
Mr Skripal is making good progress and will be discharged “in due course” but is recovering more slowly than his daughter, she added.
They were contaminated by the nerve agent novichok, thought to have been smeared hours earlier on the handle of Mr Skripal’s front door at his home on the edge of the city.
His daughter had arrived the day before on a visit from her home in Moscow.
For nearly a month both were in a critical condition, but they have recently made a remarkable recovery.
Reacting to the news Ms Skripal had been discharged, the Russian Embassy in London tweeted its congratulations but said it needed “urgent proof” that she was not being influenced.
We congratulate Yulia Skripal on her recovery. Yet we need urgent proof that what is being done to her is done on her own free will.
— Russian Embassy, UK (@RussianEmbassy) April 10, 2018
Theresa May said: “Obviously I welcome the fact that Yulia Skripal has been discharged from hospital and I wish her the best for her continuing recovery.”
When contacted on Tuesday morning Viktoria Skripal, Yulia’s cousin, said she had only just heard, via the story broken by Sky News, that her cousin had been discharged.
She has since been trying to contact her.
“I think Britain will insist that she claims asylum,” she said, adding: “I’ve tried lots of numbers for her but have had no response.
“How should I feel? I’m feeling pleased that she’s well enough to be released from hospital.
“So far my feelings are unclear because I have not seen her and nobody has seen her, we’ve just had information.”
At the end of last week Viktoria Skripal said she had been denied a UK visa to travel to Salisbury to visit her cousin and uncle.
At the end of March, Prime Minister Theresa May said doctors indicated the Skripals “may never recover fully” as she announced that more than 130 people in Salisbury could potentially have been exposed to the nerve agent.
More from Salisbury spy
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Nerve agent attack: Hopes raised Skripals could assist police investigation
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‘Miracle’ recovery: How Sergei and Yulia Skripal survived the novichok attack
The poisoning of the Skripals prompted nearly 30 countries to expel more than 150 Russian diplomats in solidarity with the UK after it blamed Russia for poisoning the family.
Russia has reacted by expelling other countries’ diplomats and closing down the US consulate in St Petersburg – after Donald Trump closed the Russian consulate in Seattle