The boats were lining up to land in Lampedusa over the past few days. Around 4,600 people from Tunisia, mostly young men, have completed the journey to the tiny Italian island since Friday, with 600 arriving Sunday, the BBC reports.
The Italian government has declared a state of humanitarian emergency and reopened a former migrant holding center on Lampedusa but the camp is overflowing.
Italy says it wants more help from the European Union and Tunisia to stem the crisis. The BBC reports that Tunisia has denied a request by Rome to allow Italian police to be deployed to the North African country, where last month's uprising forced long-time President, Zine al-Abidine Ben Ali, to quit.
Italian Foreign Minister Franco Frattini was to arrive in Tunisia this week for talks with authorities. In a telephone conversation with Catherine Ashton, the European Union's foreign policy chief, Frattini called for the EU border agency Frontex to help control the influx of migrants, Italy's La Repubblica newspaper reports.
Frontex has previously patrolled the Mediterranean waters to stop illegal migrants from reaching Spain and Italy.
The border agency is "following the situation in Italy very closely and two staff members have gone to Italy over the weekend," a Frontex spokeswoman told the BBC. "We've run many joint operations in Italy in the past. The procedure depends on what type of request we have."
A Frontex mission, however, would take weeks until it's up and running.
And even if the influx of more migrants can be stopped, there remains the question what to do with those who are already in Italy. Authorities fear that former prison inmates who fled during the unrest in the country are among real refugees looking for asylum.
A spokeswoman for the International Organization of Migration, Simona Moscarelli, said Italy should evacuate the migrants to the Italian mainland.
"It's quite a critical situation. That's why we are asking the government to organize as many trips, as many flights as possible," she told the BBC.
Others have called on other EU members to take up migrants to help Italy out. Once in the EU, some of the migrants from Tunisia might try to reach French-speaking countries where their chances for employment could be higher.
Italy, which has in the past been criticized for its handling of immigration issues, could send migrants without a job offer back to Africa.