Kiev police said on Tuesday they were investigating an attack by "far-right activists" on a Russian bank and the office of a Ukrainian politician who is close friends with Kremlin chief Vladimir Putin.

On Monday, Ukraine had marked the third anniversary of the start of three months of protests that resulted in the country's Russian-backed former president being ousted in February 2014 as the former Soviet republic set on a pro-European Union course.

The peaceful day ended with violent rallies by nationalists who at one stage firebombed and ransacked the Kiev office of the Russian bank Sberbank.