The European Union said in a resolution that members were "appalled" by the level of violence in Syria. Last week, the United Nations raised its January estimate to 70,000 dead since fighting began in Syria in 2011.
A report published Monday for the U.N. Human Rights Council said "robust" action was needed to address possible violations of international law committed by both sides in the fighting.
The U.N. Security Council has been sidelined from the debate because of veto threats from Russia, which says draft resolutions that would censure Syria lack balance.
The EU resolution said it was supporting efforts to find a peaceful resolution to the crisis.
"The EU continues to believe that the key to the solution of the conflict lies in facilitating the Syrian-led political process," the resolution stated. The EU called on Damascus to take advantage of any opportunity for political dialogue.
The push for a political resolution comes as European leaders debate an arms embargo on Syria. Bloomberg News reports British Foreign Secretary William Hague is pressing for an easing of restrictions.
Italian Foreign Minister Giulio Terzi said in a statement that Italy was "in favor of a measure that will not allow the arms embargo to expire."
Notable deaths of 2014 [PHOTOS]