Ms Politkoyskaya was found shot dead on Saturday in the lift of her apartment building in Moscow.
Authorities have pledged to hunt down the killers, but her colleagues are certain she was killed because of her critical reporting of President Vladimir Putin's war in Chechnya and expressed scepticism that authorities would ever uncover the culprits.
Prosecutor-General Yury Chaika is heading an investigation, which his office said would focus on possible links between the killing and her killers.
"I assure you that investigators and our colleagues from the Interior Ministry will do everything to ensure that the killers of Anna Politkovskaya, the perpetrators as well as those who ordered it, are found soon," spokeswoman Marina Gridneva said on state television.
In Moscow dozens of well-wishers laid flowers and candles outside Ms Politkovskaya's apartment block and her newspaper's offices.
Hundreds also rallied in Moscow's Pushkin Square to protest at both her murder and the Russian crackdown on Georgians since a spy row erupted last week.
Ms Politkovskaya's newspaper, the biweekly Novaya Gazeta, whose reporters are to investigate her death, called it a revenge killing for her coverage of Chechnya. Her editors said she was due to publish an investigative article on Monday about torture and kidnappings in Chechnya.
"We never got the article, but she had evidence about these (abducted) people and there were photographs," Deputy Editor Vitaly Yerushensky, told Ekho Moskvy radio.
Slaying condemned
US State Department spokesman Sean McCormack said the United States was "shocked and profoundly saddened by the brutal murder," and urged an inquiry -- as did a Foreign Office spokesman in London.
In Europe expressions of sorrow were joined with calls for a thorough investigation into the assassination.
French Prime Minister Dominique de Villepin described Ms Politkovskaya as a "remarkable woman, a great journalist" and called on the Russian authorities to waste no time in "shedding light" on her murder.
The French foreign minister, Philippe Douste-Blazy, said the crime "must not remain unpunished" and called on "appropriate European authorities" such as the Council of Europe to assist with investigations.
EU rights commissioner Thomas Hammarberg called for a thorough investigation, calling the crime "the signal of a major crisis for freedom of expression and for journalists' safety in Russia."
In Berlin, German Transport Minister Wolfgang Tiefensee, who knew her personally, described Ms Politovskaya as a "woman of extraordinary courage."
Spain's El Mundo newspaper blamed Russian President Vladimir Putin as "the one morally responsible for the assassination of Politovskaya" by creating a "climate of persecution" against the media.
Rights group Amnesty International believes Ms Politkovskaya was targeted "because of her work as a journalist, reporting on human rights abuses in Chechnya and other regions of the Russian Federation."
"Russia has lost a brave and dedicated human rights defender, who spoke out fearlessly against violence and injustice, and campaigned tirelessly to see justice done," said Nicola Duckworth, director of Amnesty International's Europe and Central Asia Programme.
The death brings to at least 13 the number of journalists murdered in Russia in the past six years, according to the New York-based Committee to Protect Journalists.
The last high-profile slaying was the July 2004 assassination of Paul Klebnikov, the US-born editor of the Russian edition of Forbes magazine.