"The presidency of the European Union expresses its deep concern over the murder of Russian lawyer and human rights activist Stanislav Markelov, who defended the interests of multiple victims of human rights abuses in Chechnya," the country's embassy in Russia said in a statement.
Markelov was shot dead on Monday in downtown Moscow. Novaya Gazeta journalist Anastasia Baburova, 25, was wounded in the shooting and died in hospital later on Monday.
The lawyer had protested the early release of former Russian army officer Yury Budanov.
Budanov, who commanded a tank regiment during the second military campaign in Chechnya, was convicted in the summer of 2003 of strangling 18-year-old Elsa Kungayeva three years earlier and was sentenced to 10 years in jail. He was paroled earlier this month.
Besides representing Kungayeva's family, Markelov had also started an independent investigation into a near-fatal recent attack on Mikhail Beketov, editor-in-chief of the local Khimki Pravda newspaper, who fought a campaign to protect a forest from destruction by real estate developers.
The Czech Republic also called on the Russian authorities "to investigate Markelov's murder, as well as previous attacks on human rights activists, journalists and members of non-governmental organizations, and to bring those guilty to justice."
Secretary General of the Council of Europe Terry Davis compared the murder with that of the 2006 shooting of Novaya Gazeta investigative journalist Anna Politkovskaya, and said such crimes gave grounds to doubt the reality of human rights in Russia.
"The murder of lawyer Stanislav Markelov and journalist Anastasia Baburova on the streets of Moscow is only the most recent attack on people working for human rights in Chechnya," Davis said.
"These crimes may not be connected, but until they are properly investigated by the Russian authorities and all those responsible are brought to justice, there will be a shadow over the state of the rule of law, the freedom of expression and the commitment to human rights in the Russian Federation," he went on.
German Foreign Minister Frank-Walter Steinmeier has also urged an investigation into the murder.
"Such violence towards lawyers and journalists creates an atmosphere of fear," Steinmeier's press service quoted him as saying.
The French Embassy in Russia has also condemned the attack, saying that the double murder "shows that the protection of human rights and freedom in Russia is still a day-to-day fight, which takes heavy toll on Russian citizens."
The Reporters Without Borders organization posted a statement on its website saying that the murders were the result of, "the persistent hold of violence on Russian society."
"We offer our condolences to the families of Anastasia Baburova and Stanislav Markelov," the international press freedom organization said. "Their deaths are a tragedy, resulting from the persistent hold of violence on Russian society, but also the impunity that reigns in cases of murders of journalists and human rights activists."
"The authorities must quickly hunt down, identify, and try those responsible for this double murder. Murders of journalists, lawyers and human rights defenders in Russia can only be stopped by breaking the cycle of impunity," it concluded.
The organization has said that 21 journalists were murdered in Russia between 2000 and 2007.
Meanwhile, hundreds of people, including prominent human rights and opposition activists, gathered on Tuesday at the scene of the shootings.
"Everyone who came here today wonders about the same thing - who is next?" said Alla Gerber, a member of the Russian Public Chamber and the head of the Holocaust Foundation.
Several thousand people attended a similar rally in the Chechen capital of Grozny, the Ekho Moskvy radio station reported.
