EU foreign policy chief, Catherine Ashton in her address to the UN human rights conference in Geneva, said the violence “shocks our conscience”.
BBC news have reported that tens of thousands of migrants many from Egypt are stranded near Libya’s Tunisian border.
Correspondents in Tripoli say a demonstration against Libyan leader Muammar Gaddafi is taking place in a city suburb.
The protesters, in the suburb of Tajoura, are chanting: “The blood of martyrs won’t go to waste.”
The United States has publicly backed anti-Gaddafi groups in eastern Libya.
Speaking on her way to the Geneva meeting, US Secretary of State Hillary Clinton said Washington was “reaching out to many different Libyans in the east”.
Opening the meeting, UN Human Rights Commissioner Navi Pillay warned the Libyan authorities that widespread attacks on civilians could amount to crimes under international law.
“It is a matter of great sadness that so much blood has been shed to usher in change. Let me reiterate that the illegal and excessively heavy-handed response of a number of governments is unacceptable,” she said.
Baroness Ashton said sanctions imposed on Libya by the European Union would take effect quickly.
“What is going on – the massive violence against peaceful demonstrators – shocks our conscience,” she said. “It should spring us into action.”
Earlier Russian Foreign Minister Lavrov said the use of military force against the civilian population was “unacceptable”.
“Russia condemns such violence and demands that it cease immediately, and that international humanitarian law be fully observed,” he said.
His Australian counterpart Kevin Rudd called for a no-fly zone to protect the Libyan people, and said Col Gaddafi should depart.
“The peoples of the entire world are saying go. And for the sake of humanity, go now,” he said.
At least 1,000 people are believed to have been killed during nearly two weeks of violence in which eastern cities have fallen to anti-government forces.