Britain's Culture Secretary Michelle Donelan said the IOC's move was a "world away from the reality of war".
"We condemn any action that allows President Putin to legitimize his illegal war in Ukraine," Donelan said.
"This position from the IOC is a world away from the reality of war being felt by the Ukrainian people -- and IOC president (Thomas) Bach's own words less than a year ago where he strongly condemned Russia for breaking the Olympic Truce and urged it to 'give peace a chance," she added.
The head of Denmark's National Olympic Committee, Hans Natorp, said his country was also strongly opposed to Russia's return to the Olympic fold.
"The Russian aggression in UKR is escalating," he tweeted. "Under these circumstances, it will be unacceptable to open up for RUS and Belarusian international sports participation.
"We stand firmly in our position. Now is not the right time to consider their return."
The mayor of Paris said though that she was in favor of Russian athletes competing as neutrals at the 2024 Olympics.
"I think that it's a sporting moment and we shouldn't deprive athletes of the competition," Anne Hidalgo told France 2 television on Thursday.
"But I think and what I'm arguing for, as is a large part of the sporting world, is that there isn't a delegation under the Russian banner."
She suggested they compete under a "neutral banner".
Paris organizers have no say on the participation of Russian and Belarusian athletes.
The IOC said on Wednesday that the international federation for each Olympic sport was "the sole authority for its international competitions."
Russia and their allies Belarus have been sidelined from most Olympic sports since the invasion of Ukraine last February.
But the IOC said "no athlete should be prevented from competing just because of their passport".
Hot on the heels of that announcement, the Olympic Council of Asia on Thursday offered Russian and Belarusian athletes the chance to compete in the Asian Games.
That is significant because they could gain qualifying marks in competition in Asia for the Paris Olympics.
The OAC said: "All athletes, regardless of their nationality or the passport they hold, should be able to compete in sports competitions."
Ukrainian President Volodymyr Zelenskyy is strongly opposed to any moves to reintegrate Russia into the Olympics.
Ukraine threatened Thursday to boycott the 2024 Olympics in Paris if Russian and Belarusian athletes are allowed to take part, a prospect described as "unacceptable" by the country's sports minister.
"Such a situation is unacceptable for our country," Ukrainian Sports Minister Vadym Goutzeit said Thursday.
Goutzeit said Kyiv was currently pressuring the IOC and other international organizations to gain support for the banning of Russians and Belarusians from the Olympics.
"Our position remains unchanged - as long as the war continues in Ukraine, Russian and Belarusian athletes should not be in international competitions," Goutzeit wrote on Facebook.
"If we are not heard, I do not exclude the possibility that we will boycott and refuse to participate in the Olympics."