China and Russia, veto-wielding members of the U.N. Security Council, have stopped various resolutions seeking to censure Damascus for the 11-month-old conflict.
Russia, one of Syria's main weapons suppliers, said it fears a resolution would lead to an international conflict like last year's war in Libya.
A measure passed Thursday by the European Parliament strongly urges the Kremlin to back growing sentiment that U.N. action is needed to stop the violence in Syria.
"Parliament stresses that, as a permanent member of the Security Council, Russia needs to take its responsibility for international peace and security seriously," a statement from Parliament's news service read. "It also calls on Russia immediately to halt all arms and military equipment sales to the Syrian government."
The Syrian government announced plans for a referendum on a new constitution by the end of February.
Syrian Ambassador to China Imad Moustapha told China's official Xinhua news agency that international efforts won't do anything to resolve the crisis.
"The government of Syria is deeply committed to a political solution," he said.
The United Nations said the conflict in Syria has taken on a sectarian tone, pushing the country to the brink of civil war. At least 6,000 people have been killed since the conflict began last March.