UEFA said on Saturday it was investigating the incidents which took place during the 4-1 win over the Czech Republic in the city of Wroclaw on Friday.
"Some people in the stadium carried out acts which were unworthy of real soccer fans. There is no place in the stands for people who use sporting events to declare personal, political or other points of view," the federation said in a statement on its website.
"The federation and the Russian national team strongly ask all real fans to oppose the provocative acts of hooligans and to fully cooperate with match organisers when it comes to questions of security."
European football's governing body is probing reports of alleged abuse directed at Czech players by Russia fans.
"We are appealing to all fans. Remember, you represent your country. Respect yourself, your motherland and your team," said the federation statement.
Wroclaw police spokesman Kamil Rynkiewicz told Reuters the two were detained before the start of Russia's match because "they refused to follow the orders of peace-keeping services".
They spent a night at the so-called "sobering-up tank".
