"But if the issue is with Russia or [Moscow's former Soviet ally] Belarus then here you will have a full hue and cry."
Narochnitskaya said the institute was up and running and would move into its Paris premises in the next few weeks.
The initiative coincides with a growing frustration among senior Kremlin officials who believe Western governments are using human rights as a weapon to prevent Russia from reclaiming its place as a world power.
Human rights groups and Western governments have alleged that Russian elections are not free and fair, that media freedom is being suppressed and opposition activists persecuted.
Vladimir Putin, who has stepped down as Russia's president, but is staying on as prime minister, has acknowledged his country's record is imperfect but says no country is blameless.
He has pointed to the treatment of detainees at the US-run Abu Ghraib detention centre in Iraq and Guantanamo Bay in Cuba, as well as what Moscow calls official discrimination against ethnic Russians living inside the European Union.
But political observers noted a slightly different tone on the subject in Dimitry Medvedev's presidential inaugration address on Wednesday morning.
Medvedev, who was hand-picked by Putin, said the development of "civil and economic freedom" would be the key issues covered during his term.
Medvedev said he would aim to create "new and wide opportunities of self-fulfilment for citizens, citizens who are free and responsible both for their own success and the flourishing of the entire country".
Highlighting his background as a lawyer, the president said that he would work to ensure that Russian laws are applied fairly.
At an EU-Russia summit in Portugal in October last year, Putin said he wanted to set up a Russian human rights watchdog that would operate in Europe.
Narochnitskaya said her project had no links to the government, though it was met with "a certain approval" in the Kremlin and it planned to apply for a government grant.
She said that for now the institute had modest funding from a Russian company, which she declined to name.
One of the institute's first projects was to publish a book which argues that bloodless revolutions in Georgia and Ukraine which installed pro-Western leaders were plotted and financed by the West.
Narochnitskaya said another project in development was to "monitor the monitors" who pass judgment on the fairness of elections.
Moscow has accused monitors from European democracy watchdogs of having a political agenda.
She said the institute also planned to send a fact-finding mission to Kosovo to assess if the rights of the Serb minority there are being respected.
Russia backed its ally Belgrade in opposing independence for Kosovo.