State TV announced on Wednesday evening that the conversation had taken place, saying it had been passed a recording of it by Yulia's cousin, Viktoria Skripal, and could not vouch for its authenticity.
Britain blames Russia for the nerve agent poisoning, something Moscow denies.
The attack left the Skripals in a critical condition, but on March 29 the hospital where they are being treated said Yulia was getting better, while the BBC, citing sources, said she was "conscious and talking."
State TV and Interfax said Yulia Skripal had allegedly phoned Viktoria Skripal on Wednesday evening and said:
"Everything is fine, everything is fixable, everyone is getting better, everyone is alive."
When asked about her father's health, Yulia was cited as saying: "Everything is fine, he is resting right now, sleeping. Everyone's health is fine, nobody has any problems that can't be put right. I will soon be discharging myself (from hospital)."
Viktoria Skripal, Yulia's cousin and Sergei's niece, has said she plans to travel to England and try to bring Yulia back to Russia.
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