Italian authorities are struggling to cope with a crisis on the tiny island of Lampedusa after thousands of migrants arrived from Tunisia.
A holding centre designed for 850 people is reported to be overflowing. More than 4,000 migrants are said to have arrived there in recent days.
Since Tunisia overthrew its president last month, police patrols along the coast have been patchy.
EU foreign policy chief Baroness Ashton has visited Tunis promising support.
She said the EU wanted to be Tunisia's "strongest ally" in pushing towards democracy and announced immediate new financial help of 17m euros (£14m; $23m).
Italy's Foreign Minister Franco Frattini is also due to visit the Tunisian capital.
He discussed the influx by phone with Lady Ashton and called for the EU border agency Frontex to help patrol the waters off Lampedusa, Italy's La Repubblica newspaper reports.
On Saturday, Italy declared a humanitarian emergency and called for EU assistance.
A spokeswoman for the International Organization for Migration (IOM), Simona Moscarelli, said Italy must fly migrants from Lampedusa to the Italian mainland as soon as possible.
"It's quite a critical situation. That's why we are asking the government to organise as many trips, as many flights as possible," she told the BBC's World Today programme, by phone from Lampedusa.
She described the migrants as "a mixed flow" - some were fleeing insecurity in Tunisia, following last month's uprising there, while others were seizing the chance to get to Europe to find work.
Tunisia's long-time President, Zine al-Abidine Ben Ali, quit amid a popular uprising later dubbed the Jasmine Revolution.
Frontex says it has not yet received an Italian request for help.
In the past Frontex has helped Spain to stem a flow of African migrants to the Canary Islands and Frontex currently has a police team in Greece, to stop illegal migrants entering the EU from Turkey.
A Frontex spokeswoman told the BBC that "we are following the situation in Italy very closely and two staff members have gone to Italy over the weekend".
"We've run many joint operations in Italy in the past. The procedure depends on what type of request we have," she said.
Any Frontex deployment to Lampedusa would require days if not weeks of planning, as the EU member states would have to agree on their contributions to the mission, in terms of personnel and equipment.
Italian officials said another 1,000 migrants arrived on Lampedusa on Sunday, bringing the total to more than 4,000. Most of the migrants are from Tunisia.
The small Sicilian island, which normally has a population of about 5,000 people, is closer to North Africa than the Italian mainland.
The migrants have arrived in small and overcrowded boats.
In Tunisia there have been strikes and clashes on the streets since the uprising, and many police officers have abandoned their posts, leaving what some describe as a state of lawlessness.
Italy's Interior Minister Roberto Maroni said on Sunday that Europe was not doing anything to help stop the flow of migrants and that he would request permission from Tunisia for Italian authorities to intervene.
A Tunisian government spokesperson, Tayeb Baccouche, dismissed the statement as "unacceptable", AFP news agency said.
In 2006-09 Frontex conducted patrols in the central Mediterranean, before Italy signed an agreement with Libya to block illegal migration to Europe.
In another operation, called Hermes, Frontex has conducted patrols south of Sardinia, to intercept Algerians and Tunisians trying to reach Europe.