Officer Nick Bailey "has left the hospital", said Cara Charles-Barks, chief executive of Salisbury NHS Foundation Trust.
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Skripal and his daughter Yulia, targets of the March 4 attack in the southern England city of Salisbury, remain in a critical but stable condition, she added.
Bailey said he had been "overwhelmed by the support, cards and messages" in a statement read out by Wiltshire Police Chief Constable Kier Pritchard.
"The level of support has been unbelievable and I've tried to respond to what I can, but I want to say I have really appreciated every single message," he said.
He paid tribute to the staff at Salisbury District Hospital but asked for a time out of the spotlight to recover.
Detective Sergeant Nick Bailey rushed to the aid of a Russian ex-spy targeted with a nerve agent. Source: Press Association
"I am just a normal person with a normal life, and I don't want my wife, children, family or I to be part of that attention," said Bailey.
"There are really no words to explain how I feel right now. Surreal is the word that keeps cropping up -- and it really has been completely surreal," he added.
A judge ruled earlier Thursday that blood samples from former Russian spy Skripal and his daughter Yulia could be taken for testing by the world chemical weapons body (OPCW).
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Russia denies all responsibility and the poisoning has plunged relations between London and Moscow into crisis
Pritchard said the investigation was "highly likely to take many months" as he paid tribute to Bailey.
"I have personally been amazed at Nick's strength and resilience," he said.
"He really is a credit to Wiltshire Police and the wider police family."
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