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.
The activists "destroyed furniture and apparently came away with some office equipment", the Kiev police said in a statement.
The branch's representative in Kiev told AFP that the bank remained closed on Tuesday due to damage but that none of the staff had been hurt.
The protesters also targeted the office of Ukrainian politician Viktor Medvedchuk.
The 62-year-old leads the Ukrainian Choice movement and is branded as a Russian ally by Kiev because of his personal ties to Putin.
The police said the windows of Medvedchuk's office were broken and "smoke bombs were thrown inside, which caused a fire".
Ukrainian Choice issued a statement on Tuesday saying that 1,000 "fascist youngsters" were responsible for the storming of the office.
It also said that it supported peace in Ukraine and called "on the international community to make an appropriate assessment of the radicals' attack".
Medvedchuk currently serves as a negotiator for the release of prisoners in the 31-month pro-Russian separatist conflict that has claimed nearly 10,000 lives in Ukraine's industrial east.
The Kiev police said it had launched two criminal investigations but had so far made no arrests.
Ukrainian nationalists have previously attacked Russian targets on holidays marking Kiev's split from Moscow.
Branches of at least three Russian banks were targeted during a spate of violence in February across Ukraine that coincided with the second anniversary of Moscow-backed Viktor Yanukovych being forced from office.