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Daniel Farke has left Krasnodar without coaching a match.
The German, who was appointed in January, brought along his assistants Edmund Riemer, Chris Domogalla and Christopher John.
The former Norwich manager told German media: “We have now, with great regret,” asked Krasnodar “to terminate our contracts.”
“The current political developments and the pleas of our children, wives, families and friends to come home, as well as the disappearance of all sporting prospects, led to this well thought out decision,” Farke said.
“The gravity of life has now unfortunately caught up with us.”
Russian media reported that Polish international Grzegorz Krychowia has also requested to leave Krasnodar.
Another German coach, Markus Gisdol, has left Lokomotiv Moscow. He told the German daily Bild that he could not “exercise his vocation in a country whose leader is responsible for a war.”
Andriy Voronin, a former Ukrainian international, resigned as an assistant coach at Dynamo Moscow, second in the Russian league.
“I cannot live in a country that is at war with my country,” he told the Munich-based Sueddeutsche Zeitung.
“Everything that is happening in my home country is a catastrophe, a great catastrophe, it makes me very depressed.”
Another Ukrainian, defender Yaroslav Rakitskiy, terminated his contract with Zenit St. Petersburg on Wednesday.
Brazilian defender Pablo has also left the club according to Russian media.
Krasnodar midfielder Remy Cabella, who is recovering from injury in France, revealed on social media that he will wait before returning to Russia.
Decisions by European handball and basketball federations to expel clubs from their main competitions have helped spark an exodus.
Belarusian club Meshkov Brest, bottom of their group of eight teams in the handball Champions League, has lost Polish, Slovenian and French players and Spanish and Portuguese coaches.
All of them could return if the “situation stabilises”, the club said.
Russian clubs were doing better in the 18-team Euroleague basketball.
Zenit Saint Petersburg, fifth, and CSKA, sixth, have announced the departure of foreign players for what the Moscow club described as “family and personal reasons related to the current situation.”