The amendments cover the Criminal and Administrative codes and the law on mass media.
Among other provisions, the bill enables law enforcement officers to eavesdrop on the telephone conversations of people accused of any crimes, while the earlier regulation only covered suspects involved in serious crimes.
Another clause prohibits law enforcement officials from instigating people suspected of extremism into committing unlawful acts. Tougher punishment is also stipulated by the bill for crimes committed out of motives of revenge or as part of a vendetta.
The new version of the law also prohibits the media from publishing and distributing materials on extremist organizations without specifying that they had been banned or closed down by a court ruling.
According to the draft law, slander of state officials, including accusations of grave crimes, violence against officials and hampering the work of authorities, would be considered evidence of extremism.
The Russian parliament's lower house, the State Duma, passed the bill Friday in the third and final reading.
The bill has yet to be signed by the president.