EU foreign ministers have condemned the Libyan government's violent repression of protesters.
Ministers meeting in Brussels said they deplored "the violence and death of civilians".
The EU has also expressed concern about Libya's threat to end co-operation in the fight against illegal immigration.
In the past week more than 5,000 illegal migrants from Tunisia have arrived at Italy's Lampedusa island, in the wake of Tunisia's revolution.
Lampedusa - a tiny island in the Mediterranean between Tunisia and Italy - is a major entry point to Europe for immigrants from Africa.
Call for dialogue
"The legitimate aspirations and demands of people for reform must be addressed through open, inclusive, meaningful and national Libyan-led dialogue," the EU ministers said in a statement released after their meeting.
The President of the European Council, Herman Van Rompuy, said separately that he was "horrified by the growing number of human casualties among demonstrators".
But there was also anxiety, especially from Italy, about the effect of prolonged instability on the EU's southern maritime border in the Mediterranean.
Italy's Foreign Minister Franco Frattini voiced alarm as reports came in that anti-government protesters had taken control of Libya's second city, Benghazi.
"I'm extremely concerned about the self-proclamation of the so-called Islamic Emirate of Benghazi," Mr Frattini told reporters. "Would you imagine to have an Islamic Arab Emirate at the borders of Europe? This would be a really serious threat."
Ministers held preliminary talks on Monday on an economic and trade package for countries in North Africa affected by the turmoil.
Mr Frattini said Europe needed to provide the equivalent of the Marshall Plan at the end of World War II - referring to the US-led reconstruction programme for Europe.
It was a view echoed by others at the meeting.
European Union tested
"I think it is an historic test for the European Union," said Britain's Foreign Secretary William Hague. "If we can succeed in bringing both more democracy and more stability to North Africa and to the wide Middle East then that would be the greatest achievement of the European Union since the enlargement of the EU."
"If we don't succeed in that," he said, "then the dangers to the European Union of instability or extremism on our frontiers are immense."
The violence has prompted European governments to prepare evacuation plans for their citizens in Libya.
Meanwhile, experts from EU member states will be deployed along with aerial and naval support to assist the Italian authorities in Lampedusa, the European Commission says.
"Frontex experts will assist in debriefing and interviewing migrants. Special attention is given to identifying those who may be in need of international protection. Frontex will also give aerial and naval support for border surveillance," EU Home Affairs Commissioner Cecilia Malmstroem said.
The government of Col Muammar Gaddafi warned the EU last week that it would stop co-operating on illegal migration from North Africa if the EU backed anti-government protesters in Libya.
In recent years, Italy and Libya have co-operated to intercept boatloads of illegal migrants in the Mediterranean. Italy has sent many of them back to Libyan detention centres - a practice condemned by human rights groups.
The number of such boats heading for Italy from Libya has declined sharply since the controversial policy took effect.
Some of the ministers in Brussels dismissed the Libyan threat.
"The European Union should not let itself be blackmailed (by Gaddafi)," said Werner Hoyer, Germany's Deputy Foreign Minister.