"This is being treated as a major incident involving attempted murder by administration of a nerve agent," said Mark Rowley, who heads Britain's counterterrorism policing.
"We believe that the two people originally who became unwell were targeted specifically," he added.
Rowley also said that a police officer, one of the first on the scene, was in serious condition in hospital.
On Sunday afternoon, Sergei Skripal, 66, and his daughter Yulia, 33, were found unconscious on a bench in the center of Salisbury, a cathedral city about 90 miles southwest of London. The two were rushed to a hospital, where they remain critically ill.
Skripal, a former Russian spy, was jailed in 2006 for passing state secrets to Britain. He was released in 2010 as part of a high-profile spy swap.
Police did not specify what nerve agent they think was used or how it was administered. Because nerve agents are complex to make, they are typically not made by individuals.
"It's what we call a state-level weapon. It's difficult to make unless you have large laboratories you'd expect to be associated with countries," said Malcolm Sperrin, a medical physics expert.
The best known nerve agents are VX, absorbable through the skin, and sarin, which tends to be inhaled or ingested. Some nerve agents have antidotes, but they need to be administered quickly to be effective.
The nerve agent VX killed Kim Jong Nam, the estranged half brother of North Korean leader Kim Jong Un. He died last year after a bizarre attack at a Malaysian airport in which VX was smeared on his face.
In April 2017, sarin was used to kill more than 80 people in the Syrian town of Khan Sheikhoun.
British police stressed Wednesday that there was a low risk to the wider public in connection with the Salisbury incident but added that specialist officers in protective clothing would be continuing their work in the city.
The incident threatens to ratchet up tensions between Britain and Russia. On Tuesday, the British foreign secretary, Boris Johnson, said that the Skripal case had "echoes" of what happened to Alexander Litvinenko, a former KGB operative who British officials believe was poisoned in London by Russian agents.
Responding to a question about the case, the Russian Embassy in London said it had received no information about the substance of the case and criticized Johnson's response as "strongly anti-Russian."
The police also appealed to members of the public who had visited Salisbury town center on Sunday afternoon, including the Zizzi restaurant and Bishop's Mill pub, which the two Russians reportedly visited.
"Our role now of course is to establish who is behind this and why they carried out this act," Rowley said.
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