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Frank Ross told a virtual meeting of the full council that the Ukrainian flag was flying above the City and he had sent a letter of support to Mayor Vitaliy Klitschko.
Edinburgh and Kyiv have been twinned since 1989.
In his letter, Councillor Ross said he was writing on behalf of the people of Edinburgh to express “deep sorrow” at the events unfolding in Ukraine.
He continued: “During the pandemic our cities have supported each other, and rest assured that as a city, I want to offer Edinburgh’s future unqualified support for Ukrainian independence, sovereign integrity, and to reassure you that we stand in solidarity with you and your people.
"This is a difficult and deeply troubling time for Kyiv, your city, Edinburgh’s cherished twin city and the capital of the democratic independent country of Ukraine. Again, I want to assure you that we stand ready to provide whatever support we can, as we have since our twinning in 1989.
Finally, we hope that you, your family and your citizens remain safe, and the current conflict will be resolved peacefully in the near future.”