In their joint statement on Monday, the International Helsinki Federation for Human Rights (IHF) and the Moscow Helsinki Group (MHG) said Vladimir Putin's silence on the killing amounted to complicity.
Speaking after the statement was issued, Putin said that all necessary measures would be taken to find the killers.
Ulrich Fischer, the IHF president, said in the statement: "The silence of President Putin suggests an attitude of complicity, or of indifference. No one can accept that, after the country's leading media critic of the government has been murdered, apparently by a professional assassin, he keeps silent."
The Vienna-based IHF and its sister organisation MHG said that they were "concerned the murder will further intimidate independent journalism in Russia".
Johann Fritz, head of the media watchdog International Press Institute, also criticised Russia's press environment.
Fritz said: "Several journalists are killed every year in Russia because of their work. Many more are violently attacked. Few of the assailants have been found and punished, which sends an unsettling message to the world about the Russian government's indifference towards press freedom.
"We call on the Russian authorities to ensure that there is a thorough investigation and that those responsible are swiftly brought to justice."
Ursula Plassnik, the Austrian foreign minister, also demanded on Monday that the Russian authorities solve the killing quickly.
"This is a despicable crime. I expect a quick and comprehensive investigation by the Russian authorities into the murder. Independent and critical journalists should not be intimidated or muzzled in a democratic state," she said.
Politkovskaya, the 48-year old award-winning journalist, who was known for her prize-winning coverage of atrocities during the war in Chechnya and criticism of the government, was shot in her apartment building in Moscow on Saturday evening.
In 2001, she sought refuge in Vienna for several months after receiving death threats.