LONDON — Russian television broadcast a telephone recording on Thursday said to be of Yulia Skripal, who was poisoned with a military-grade nerve agent a month ago and is at the center of an escalating confrontation between Russia and Britain.

In the recording, which the Rossiya 24 news announcer emphasized could not be verified, Ms. Skripal tells her cousin Viktoria that both she and her father, Sergei V. Skripal, are healthy, and that neither of them has suffered long-term health damage from the poisoning. The recording contradicted public statements by the British authorities, who have described Mr. Skripal’s condition as “critical but stable” and said that only Ms. Skripal was conscious.

Within hours of the program’s broadcast, the British police released a statement on Ms. Skripal’s behalf, in which she said that she “woke up over a week ago now” and that her “strength is growing daily.”

The two accounts underline a challenge Britain is facing as it endeavors to build and maintain an international coalition around the poisoning while keeping much of its evidence secret.