In recent days, the French police have been rounding up Northern Africans and sending them across the border to Italy, the EU country which the new arrivals reached first.
In the EU's perspective, however, such actions are illegal.
Speaking to the press on Friday (1 April), Home Affairs Commissioner Cecilia Malmström said France had no right to return the immigrants to Italy.
"In principle 'no', the French authorities cannot send them back to Italy," Malmström said, adding that according to the rules of the Schengen border-free area, de facto no border existed between France and Italy.
"France could evoke a serious threat to public order, but this is not the case here," Malmström said, referring to the Schengen agreement's stipulation that one member country can temporary shut its border under exceptional circumstances.
From Lampedusa, immigrants are taken to camps on the Italian mainland and thousands of them then make the journey to France, where they have family connections.
A 700,000-strong Tunisian community is well-established in France and relatives there help them to find shelter and employment on the black market when they arrive.
Several statements by high-ranking officials have added to the tension. Italian Prime Minister Silvio Berlusconi threatened to "grant temporary permits" to migrants who say they want to join family in France, Germany and other EU countries. Italian Foreign Minister Franco Frattini complained last week that France was failing to show solidarity with Rome.
Berlusconi today (4 April) travels to Tunisia, in an attempt to persuade the country's new authorities to prevent the departure of migrants. Italy is exploring the possibility of sending back illegal immigrants in large numbers. Rome is reportedly at present only able to do so for groups of 3-4 people.
Malmström also said that the EU was exploring the possibility of admitting to its territory several thousand displaced Somalis and Eritreans, who have escaped war-torn Libya and are now stranded at the country's borders with Tunisia and Egypt.
The sub-Saharan nationals cannot return to their home countries, she explained. Negotiations were underway with those EU countries willing to take some of them in to their territory, she said. Sweden, Malmström's home country, had promised to take 200 of them, she said.
In the meantime, a UN official said that more than 400 African migrants seeking to travel to Italy on two vessels were feared drowned.
Two boats that reportedly set out from Libya on 22 and 25 March, one carrying 335 Eritreans and the other 68 Eritreans and Ethiopians, have disappeared.
"We are urging the coastguard to carry on searching since even after 20 days at sea, some people can survive," Laura Boldrini, a UN spokeswoman, is quoted by the Guardian as saying.
