Skripal, 66, was found slumped on a shopping center bench in Salisbury, southern England, with his daughter Yulia Skripal, 33.
Skripal is a former Russian double agent, who was convicted in Russia after spying for the UK.
Once a colonel in Russia's GRU military intelligence service, he was given refuge in Britain after he was exchanged in 2010 for Russian spies caught in the West as part of a Cold War-style swap in Vienna.
Police said both were unconscious when they were discovered on Sunday afternoon.
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Both are critically ill in hospital and UK police are trying to find out what "unknown substance" harmed the pair, report said.
It has also emerged that two police officers dealing with the incident were treated for "minor symptoms", the report said.
Skripal's wife, son and older brother have all died in the past two years.
The case has drawn inevitable comparisons to the poisoning of former Russian spy Alexander Litvinenko, who died a slow death after meeting a contact at a London sushi restaurant in 2006.
Police are looking for similarities between the cases and the modus operandi used, the Independent reported.
Meanwhile, Russia today insisted it had "no information" on what could have led to the incident, but said it was open to co-operate in the police investigation if requested.
Dmitry Peskov, Russian President Vladimir Putin's spokesman, told journalists that Moscow was prepared to help with the investigation.
"We see this tragic situation but we don't have information on what could have led to this, what he was engaged in," he said.
A woman who saw Skripal and his daughter described the couple as appearing "out of it." Freya Church, a local resident, said she saw the pair on a bench. "She sort of leant in on him, it looked like she'd passed out maybe. He was doing some strange hand movements, looking up to the sky," Church said.
"I felt like I should step in but to be honest they looked so out of it that I thought that even if I did step in I wasn't sure how I would help. So yeah, I just left them, but it looked like they'd been taking something quite strong."
Temporary Assistant Chief Constable Craig Holden said: "They are currently being treated for suspected exposure to an unknown substance."
He said the police's "major incident" response was not a counter-terrorism investigation - but that multiple agencies were involved and they were keeping an "open mind".
Meanwhile, police have closed the nearby Zizzi restaurant "as a precaution".
Holden said police were keeping an open mind on the cause of injuries. He said the incident was not being treated as terrorism and cautioned against speculation.
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