0131 GMT February 19, 2020
In one of the most momentous moves in its chequered history, the International Olympic Committee said Sunday it was up to each international sports federation to decide if Russians could take part in Rio, AFP reported.
The federations now face a race against the clock with the opening ceremony only 11 days away, global sport sharply divided and some Russian competitors already in Brazil.
Kremlin spokesman Dmitry Peskov called the IOC decision "positive".
"We welcome the main decision, which allows so-called clean athletes to take part in the Olympic Games," Peskov told reporters.
Russian sport and the Kremlin have been rocked by doping scandals that saw its track and field team banned from competition, including Rio, and sparked calls led by the World Anti-Doping Agency (WADA) for all Russians to be barred until they cleaned up.
Dmitry Svishchev, who heads the lower house of Russian parliament's sports and physical culture committee, told AFP the IOC decision was "not bad".
But he railed against the ban — still in force — meted out previously to the athletics team.
"You can't punish twice for the same thing," Svishchev said.
World champion hurdler Sergey Shubenkov, who cannot take part in Rio as a consequence, tweeted that Sunday's IOC ruling was "hard but reasonable".
Pro-Kremlin tabloid Komsomolskaya Pravda said the IOC had taken the "safest route for itself".
Russia's gymnastics team — the first group of Russian athletes to arrive in Rio for the Games — are already training in Brazil, coach Valentina Rodionenko told R-Sport news agency, saying that "the worst is behind us".
Most Russian competitors will fly out on Thursday, R-Sport reported, although it remains to be seen how many will actually take part in the Games.
'A black day'
The reaction was in stark contrast to much of the rest of the world.
Olympic chiefs had been under pressure — and with time running down to Rio — to hit Russia with the hardest sanctions possible to punish state-run doping that was laid bare in a WADA-commissioned report a week ago by professor Richard McLaren.
It revealed wide-ranging Russian doping in Olympic events from 2011 and including the Sochi Games in 2014, where the secret service used a hole drilled in a wall to swap the dirty samples of doping competitors for clean ones, under the noses of international observers.
Four-time Olympic rowing champion Matthew Pinsent led a cacophony of British condemnation.
"IOC has passed the buck — pure and simple," wrote the 45-year-old Pinsent in The Times.
Defending Olympic long jump champion Greg Rutherford also weighed in.
"(The IOC's decision) is a spineless attempt to appear as the nice guy to both sides," the 29-year-old told the Guardian newspaper.
The Australian government warned that a "suspicion of compromised integrity" now hung over the Games and New Zealand's anti-doping body lamented "a black day for clean athletes".
That came after WADA president Craig Reedie said, "The McLaren report exposed, beyond a reasonable doubt, a state-run doping program in Russia that seriously undermines the principles of clean sport embodied within the World Anti-Doping Code."
US anti-doping chiefs blasted the IOC for creating "a confusing mess".
'She got what was coming'
Thomas Bach, the IOC president, said the Olympic body had faced an extremely difficult decision and had to "find the balance between the overall responsibility (of Russia) and the rights of each individual athlete".
"The decision will certainly not appeal to everyone, but it comes down to justice," Bach said in the immediate aftermath on Sunday.
The focus will now be on the Olympic sports to let in Russians who they believe are drug-free.
The World Archery Federation quickly declared that three Russian archers who had never tested positive for banned substances would be allowed to compete in Rio.
Russia's fencing and pentathlon federations have expressed confidence that Russian athletes in their respective sports will also take part, but were still awaiting an official confirmation from the respective federations.
Russian media meanwhile praised the decision not to allow Russian whistleblower Yulia Stepanova, who exposed mass doping in athletics, to compete at Rio.
The 800m runner, whom the IOC banned from participating even as a neutral, "got what was coming to her", Komsomolskaya Pravda wrote.