Riot police killed the alleged rebels early on Saturday in Chechnya's southern district of Urus-Martan, a spokesman for Chechnya's interior ministry said.
He said that the three were killed when they refused to surrender.
Officials said that a large arms cache was found in the suspects' home and that investigators were working to determine the identity of the men.
Putin's birthday rally
In Grozny, the Chechen capital, several thousand young people held a tightly choreographed rally to celebrate the Russian president's 54th birthday.
The event was staged by Chechnya's Moscow-backed authorities who are eager to demonstrate their loyalty to the Kremlin.
Many of the high school and college students who attended the rally said they had been forced to. One Chechen girl called a local radio station earlier in the week, telling the host that she and fellow students were being forced to attend by education officials.
Those attending wore t-shirts emblazoned with portraits of Putin and many waved Russian flags.
There were banners wishing Putin "health, happiness and success in work" and people chanted "Putin, congratulations".
One student read a poem in which she asked Putin to stay in power after his second term expires in 2008.
Putin is constitutionally barred from running for a third term, but supporters and various regional groups, including in Chechnya, have called for a referendum on amending the law to allow Putin to stay in power.