It would be "difficult to see" how England could participate in the tournament if Vladimir Putin's Russia was behind the poisoning of Skripal, Johnson said on Tuesday.
The 66-year-old former Russian intelligence official was taken ill at a shopping centre in Salisbury, south England. He and his daughter are both in intensive care at Salisbury District Hospital.
"They are currently being treated for suspected exposure to an unknown substance. Both are currently in a critical condition in intensive care," police said on Monday.
Skripal was granted asylum in Britain after being pardoned by Russia in a 2010 "spy swap" deal with the US, under which 10 Russian spies arrested by the FBI were released.
The ex-Russian military intelligence colonel was jailed by Moscow for 13 years after passing the identities of Russian intelligence agents working in Europe to the UK's Secret Intelligence Service, MI6, the BBC said.
Some observers have already drawn comparisons with Alexander Litvinenko, the former KGB spy who was poisoned in a luxury London hotel in 2006. He drunk tea poisoned with a rare radioactive isotope and, from his deathbed, accused Russian President Vladimir Putin of ordering his murder.
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