Nicolas Sarkozy and Silvio Berlusconi are expected to call on Tuesday for a partial reintroduction of national border controls across Europe, a move that would put the brakes on European integration and curb passport-free travel for more than 400 million people in 25 countries.

The French president and the Italian prime minister are meeting in Rome after weeks of tension between their two countries over how to cope with an influx of more than 25,000 immigrants fleeing revolutions in north Africa. The migrants, mostly Tunisian, reached the EU by way of Italian islands such as Lampedusa, but many hoped to get work in France where they have relatives and friends.

Earlier this month, Berlusconi's government outraged several EU governments, including France, by offering the migrants temporary residence permits which, in principle, allowed them to travel to other member states under the Schengen agreement. An Italian junior minister said on Sunday that Rome had so far issued some 8,000 permits and expected the number would rise to 11,000.

Launched in 1995, Schengen allows passport-free travel in most of the EU, Switzerland, Norway and Iceland. But the documents issued by the Italian authorities are only valid if the holders can show they have the means to support themselves, and French police have rounded up or turned back an unknown number of migrants in recent days.

On 17 April, Paris blocked trains crossing the frontier at Ventimiglia in protest at the Italian initiative. "Rarely have the two countries seemed so far apart," said Le Monde in an editorial on Monday.

Yet, with both leaders under pressure from the far right, French and Italian officials appear to have agreed a common position on amending Schengen so that national border checks can be reintroduced in "special circumstances".

According to a report from Paris in the Italian daily La Repubblica, the two countries would also press for an increase in EU assistance to those countries that have to cope with immigrant influxes – a key Italian demand.

On Saturday, Berlusconi's spokesman said: "Agreement has been reached." Indications of a deal have prompted outrage from the French opposition. Harlem Désir of the Socialist party said: "Sarkozy and Berlusconi are disgracing Europe."

A joint initiative would certainly be an historic departure for two countries that have long been regarded as among the most fervently "European".

Schengen is seen as the EU's most significant integration project after the euro. Now both are under pressure, a sign of the tensions eating away at the union.

Sarkozy, low in the polls and hoping for re-election next year, is threatened by the Front National and its leader, Marine Le Pen, who calls for the total scrapping of Schengen.

Berlusconi, whose poll ratings have also been sliding, is dependent for his majority in parliament on the xenophobic Northern League, one of whose leaders, Roberto Maroni, is Italy's interior minister.

Even before the exodus from Tunisia, gains by far-right, anti-immigrant parties in north Europe had put Schengen under strain. Centrist parties in Germany, Austria, Belgium and the Netherlands have all tried to appease the far right by threatening to re-erect national border controls.

EU interior ministers are to meet on 12 May to try to resolve the issue. A joint Franco-Italian demand would need to be endorsed at EU level.

It has been framed against a background of mutual exasperation with Greece over its difficulties in policing its frontier with Turkey, an EU external border thought to be the main crossing point into the union for clandestine migrants.

Seaborne migration to islands such as Lampedusa, though highly visible, accounts for only a fraction of the total number of illegal entries.

Italy, however, is concerned that an end to the hostilities in Libya could prompt a renewed surge in attempted crossings by people who would not necessarily want to move to other EU states. Alfredo Mantovano, the junior interior minister responsible for immigration, said "the number of people involved could be 50,000".