During a post-European Union summit news conference, Putin also said Chechen rebels want to kill all non-Muslims and establish an Islamic state in Russia.
Putin became agitated Monday after a reporter from the French newspaper Le Monde questioned his troops' use of heavy weapons against civilians in the war in Chechnya. Chechnya is predominantly Muslim.
"If you want to become an Islamic radical and have yourself circumcised, I invite you to come to Moscow," Putin said.
"I would recommend that he who does the surgery does it so you'll have nothing growing back, afterward," he added. Circumcision is a tenet of Islam for all males.
Because of poor translation, Putin's remarks were not immediately understood by either the 450 journalists present at the news conference Monday or by senior EU officials. The Russian president brought his own interpreters, and even the native Russian speakers were unable to keep pace with Putin's rapid-fire delivery.
Details of what Putin said were revealed Tuesday when The Associated Press translated an audiotape from the news conference. As a result, there was a little coverage of Putin's remarks in the European media on Tuesday.
EU spokesman Jonathan Faull, who was not at the press conference, said that if reports of Putin's remarks were true they were "entirely inappropriate."
Gunnar Wiegand, also a EU spokesman, said it was not the job of EU officials to take responsibility for comments by foreign dignitaries. Russia is not a member of the European Union.
Wiegand said Putin used "decidedly less robust" language when speaking with EU leaders about the Chechen war and human rights in the breakaway province.
The translation showed Putin issuing a broadside against the Chechen rebels.
"They talk about setting up a worldwide (Islamic state) and the need to kill Americans and their allies," Putin said. "They talk about the need to kill all...non-Muslims, or 'crusaders,' as they put it. If you are a Christian, you are in danger.
"If you decided to abandon your faith and become an atheist, you also are to be liquidated according to their concept. You are in danger if you decide to become a Muslim. It is not going to save you anyway because they believe traditional Islam is hostile to their goals."
In Moscow, the daily Kommersant said the EU-Russia summit "ended in a serious scandal" because of Putin's comments, which Kremlin aides said were made in response to a "provocative question."
Gazeta.ru, a leading online publication in Moscow, quoted unidentified Putin aides as saying the president was tired and angry after being peppered with questions about Chechnya.
Putin owes his quick rise in the Russian power structure to his tough handling of the Chechen war, which has been sharply criticized by many in the West.
Putin claims Russia is fighting international terrorism - not an independence movement - in Chechnya. He calls Chechen fighters "religious extremists and international terrorists" whose impact has spread far beyond the borders of the republic.
He pointed to last month's hostage-taking in a Moscow theater by Chechen rebels. Russian special forces troops stormed the auditorium after three days, pumping a knockout gas into the theater to disable the rebels, all of whom were killed.
At least 128 of the approximately 750 hostages died, most from the disabling gas.
Putin praised Russian handling of the crisis and said other nations must adopt a similarly tough stand against terrorism to prevent further incidents like it and the recent bombing of tourist nightclubs in Bali, Indonesia, where about 200 people were killed.
EU officials said Tuesday they had made "strenuous efforts" but failed to win Putin's signature on a joint declaration on Chechnya. The Russian leader refused to sign because the document referred to human rights in the republic.
By Robert Wielaard