Mr Khan also pointed out that nobody thought that Slobodan Milosevic, the Serbian leader who went on trial for war crimes in Croatia, Bosnia and Kosovo in the 1990s, would end up in The Hague to face justice.
"Those that feel that you can commit a crime in the daytime, and sleep well at night, should perhaps look at history," Mr Khan said.
Kremlin spokesman Dmitry Peskov said any of the court's decisions were "null and void" and former Russian President Dmitry Medvedev compared the warrant to toilet paper.
Russian opposition activists have welcomed the announcement. Ivan Zhdanov, a close ally of jailed opposition leader Alexei Navalny, has tweeted that it was "a symbolic step" but an important one.
Ukrainian President Volodymyr Zelensky has expressed his thanks to Mr Khan and the ICC for their decision to press charges against "state evil".