Delegates say they want to send a message to the G8 governments that the fight against terrorism must not come at the expense of human rights and democracy.
The Moscow Helsinki Group, Memorial, and Amnesty International are among the groups attending the conference.
Later today, religious leaders from more than 40 countries are expected to open a separate Faith Summit in Moscow. Organized by the Russian Orthodox Church, the meeting will focus on the role of religion in society and the protection of moral values.
The Vatican delegation will be headed by Cardinal Walter Kasper, head of the Vatican's Council for Christian Unity.
(AP, AFP, ITAR-TASS)
MORE: For more coverage of this topic from RFE/RL's Russian Service in Russian, click here.