Moscow also suspects foreign governments of trying to influence the outcome of next year's presidential election.
Also present at the meeting was Vladimir Lukin, a former Russian ambassador to the US who is Russia's state human rights ombudsman.
National television, the main source of news for most Russians, has come under tighter Kremlin control and opponents of Vladimir Putin, the president, now rarely have access to the airwaves.
Rice said: "I am quite confident that your goal is to build institutions that are indigenous to Russia - that are Russian institutions - but that are also respectful of what we all know to be universal values."
"The rights of individuals to liberty and freedom, the right to worship as you please, and the right to assembly, the right to not have to deal with the arbitrary power of the state."
But Tatyana Lokshina of Demos, one of the eight campaigners who met Rice, said after the meeting she had warned the secretary of state that Washington had lost moral authority, "considering the Iraq war, the Guantanamo problem and the Abu Ghraib scandal".
Though the US and other Western governments have voiced concern about democracy in Russia under Putin enjoys strong public support.
Rice arrived in Moscow on Friday for talks on strategic issues, including US plans to build a missile defence shield in parts of central Europe. A plan Moscow opposes.
She is set to met media, civil society and business leaders later on Saturday.