By Dmitry Solovyov and Dmitriy Rogovitskiy

MOSCOW (Reuters) - The Kremlin on Monday hailed a decision by the International Olympic Committee not to ban Russia's entire team from the Rio Olympics over doping allegations, but government officials said the strings attached to the IOC's ruling were unfair.

The IOC threw Russian sportsmen and women a lifeline on Sunday ignoring a call from the World Anti-Doping Agency to impose a blanket ban, ruling instead that decisions on whether individual competitors could compete at Rio would be left to the international sports federations.

That prompted a sigh of relief in Moscow where President Vladimir Putin had spoken of a possible schism in the Olympic movement and complained of what he said was growing Cold War-style political interference in sport.

The scandal, which centers on allegations that the Russian government and FSB security service have systematically covered up doping in sport, has hurt Putin's attempts to tie Russia's sporting prowess to what he says is his country's resurgence on the world stage, but his own ratings look safe.

Dmitry Peskov, Putin's spokesman, said on Monday that Putin would not be attending the opening ceremony of the Rio games, but that the Kremlin was pleased with the IOC ruling.

His comments echoed those of other senior officials who said they believed that common sense had prevailed over what they said looked like a witch hunt.

"Certainly, we welcome the main decision which allows so-called clean athletes to take part in the Olympic Games, given the permission of international (sports) federations," Peskov told reporters on a conference call.

The IOC ruling came with a twist however that angered some Russian government officials, stipulating that any Russian athletes sanctioned for doping in the past would not be eligible to go to Rio.

Alexander Zhukov, the head of Russia's Olympic Committee, said that smacked of double standards as sportspeople from other countries with a history of doping would be allowed to compete.

"Why are only Russian sportsmen being punished in this way?" Zhukov said in televised comments. "This flouts the principle of equality (of treatment)."

Zhukov said 13 members of Russia's Olympic team had a doping history, according to the R-Sport news agency.

Russia's track and field athletes, already barred from the games over the doping scandal, are not affected by the IOC ruling and, with the possible exception of one athlete based in the United States, will not be competing.

Russian Sports Minister Vitaly Mutko sent a letter on Monday to the International Association of Athletics Federations, asking it to reconsider this blanket ban, the R-Sport news agency reported. [R4N1A6014]

Other athletes, with no doping history, who have been cleared by global sporting federations, will be competing.

Russia's three-member archery team was cleared on Monday to take part by the World Archery Federation, while all seven Russian tennis players were cleared by the International Tennis Federation on Sunday.

There was bad news for Russia's swimmers though, with FINA, the World Swimming Federation, saying on Monday it had decided that seven Russian swimmers were ineligible.

(Writing by Andrew Osborn; Editing by Robin Pomeroy/Richard Balmforth)