The New York-based group said on Monday Russian security forces were continuing to commit "crimes against humanity" in the rebellious Caucasian region, where thousands of people have disappeared in the past six years.
"It is astounding that the European Union has decided to take no action on Chechnya," Rachel Denber, the group's acting executive director for Europe and Central Asia, said in a statement.
"To look the other way while crimes against humanity are being committed is unconscionable."
Brussels has usually spearheaded efforts to condemn alleged abuses by Russian security forces in Chechnya, but EU foreign ministers decided last week to make no such move at the annual session under way at the UN's European headquarters in the Swiss city of Geneva.
The last time the 53-state rights commission voted to criticise Moscow over its policies in Chechnya was in 2001. Last year's EU resolution was soundly defeated.
European diplomats say Brussels will continue to express its concerns directly to the Russian government. The EU will also deliver a statement critical of Moscow later in the six-week session, which runs until 22 April, they added.
Putin's Chechnya policy is taking
its toll on security forces as well
Brussels has also decided against any new attempt to pillory Zimbabwe over accusations of widespread repression of government opponents for fear it could be used as political ammunition by President Robert Mugabe in the 31 March parliamentary elections, diplomats say.
In Chechnya, Human Rights Watch said a recent mission to the region found dozens of new cases of people being detained by Russian security forces and never heard of again, despite assertions by Moscow that the situation in the region was being "normalised".
The Russian government presents its fight to pacify the separatist region as being part of the US-declared "war on terrorism".
Scale of problem
Among the victims listed in a 57-page report were 22-year-old student Adam Demelkhanov and carpenter Badrudin Kantaev, 44, who were both detained by soldiers in armed personnel carriers in the village of Starye Atagi in November 2004.
"To look the other way while crimes against humanity are being committed is unconscionable"
Acting Executive Director for Europe and Asia,
Human Rights Watch
Local human-rights groups estimated that 3000-5000 people had disappeared since the beginning of the latest conflict in 1999.
Even Russian official statistics put the figure at over 2000, Human Rights Watch added.
The vast majority of these "disappearances" were carried out by Russian government agents, either federal forces or, increasingly, local Chechen security forces, it said.
"The Russian government is fully aware of the scale of the problem," Denber said.
"It simply isn't committed to bringing the perpetrators to justice," she added.