Six Shakhtar players, all from South America, have refused to report back to the club for the new season, citing safety concerns. Some are now reportedly in talks to transfer to clubs in other European countries.
Ukraine's other representative in the Champions League -- Europe's top club competition -- is Dnipro Dnipropetrovsk, which is playing its home games in the capital, Kiev. Its first European match of the season -- a third-round qualifying game against FC Copenhagen -- was interrupted by crowd violence Wednesday, prompting a UEFA investigation.
Since Russia annexed the Crimean Peninsula in March, it has registered a total of five new clubs there.
Sergei Stepashin, a former Russian prime minister who sits on the RFU executive committee, told local media that "sanctions are possible" if Russia incorporates the Crimean clubs, but that the organization had "no doubts" it was the right thing to do.
Asked about possible sanctions against the Russians, Ternnovoi said the Ukrainian federation "doesn't want the destruction of Russian football."
"The federation wants justice and the absence of politics in football, both in Russia and in Crimea," he said.
The RFU wants Sports Minister Vitaly Mutko, a FIFA executive committee member, to lobby FIFA President Sepp Blatter on the issue, Stepashin said.
FIFA and UEFA offices in Switzerland were closed Friday, a national holiday. Attempts to reach officials for comment were unsuccessful.
Some European politicians, including British Deputy Prime Minister Nick Clegg, want Russia removed as host of the 2018 World Cup. But FIFA has stood by Russia, saying the tournament "can achieve positive change" in the country. FIFA President Sepp Blatter had already rejected calls to strip Russia of the tournament after it annexed Crimea.
Russian World Cup organizers have previously said Crimea could host team training bases during the tournament.
While eastern Ukraine has been engulfed by fighting between the Ukrainian army and pro-Russian rebels, Crimea has remained peaceful and fully under Russian government control.
With more than 1,000 people killed -- including the 298 passengers and crew of Malaysia Airlines Flight 17 -- and many more displaced, the conflict in eastern Ukraine has touched all aspects of everyday life. Last week, Ukrainian Premier League club Zorya Luhansk, whose home city is the base of a pro-Russian group, posted pictures of damage to its stadium caused by mortar rounds that smashed seats and left a crater in the field.
Tavria shares its name with a former Ukrainian champion club renowned as a hotbed of pro-Ukraine sentiment in Crimea, especially among its hardcore fans. Even after the annexation, Tavria and fellow Crimean team FC Sevastopol played out the remainder of the season in the Ukrainian Premier League, but have now been replaced by new Russian-registered entities.
In the second division south, the Crimean clubs will face a mixture of once-major Russian clubs fallen on hard times, such as former national champion Alania Vladikavkaz, local semi-professional clubs and reserve teams for Premier League sides.
Playing in tiny Russian provincial stadiums represents a step down for longtime Tavria fans, whose team was playing Europa League soccer as recently as the 2010-11 season.