Russia's lower house of parliament approved the bill Friday and it came into effect after being published in newspapers.
The law, proposed by President Vladimir Putin, is a follow-up on the Kremlin's offer of a fair trial for cooperative militants in Chechnya and other parts of the restive North Caucasus region.
But a senior member of the State Duma said Friday the amnesty did not extend to members of illegal armed groups who committed grave crimes, including hostage-taking and terrorist attacks.
"Besides, the amnesty does not cover military servicemen involved in the theft or illegal sale of weapons or similar crimes," said Pavel Krasheninnikov, head of the State Duma's Civil, Criminal, Arbitration and Procedural Law Committee, and a former justice minister.
Krasheninnikov also said earlier the amnesty did not cover foreigners and stateless persons.
The amnesty will be in force for six months from the date of its publication.
Krasheninnikov said courts will decide on pardons for former militants now on trial, whereas investigative bodies will make decisions on persons still under investigation. He added that while surrendering, former militants should turn in their arms and equipment.
An appeal to surrender was made after the killing of the region's number one terrorist Shamil Basayev in July, and was initially valid until August 1, with the deadline later extended to September 30.
Nikolai Patrushev, head of the National Antiterrorism Committee, said Thursday about 300 militants have accepted the surrender offer since its announcement July 15, most of them in Chechnya.