LUXEMBOURG—Interior ministers from France and Italy tried Tuesday to end a dispute over the movement of immigrants from Africa and the Middle East, as European Union ministers continued to grapple with the illegal migration problem facing the 28-nation bloc.

The two countries have been arguing over the thousands of migrants that Italy has allowed to travel to France in recent months, many of which have been sent by the French authorities back to Italy. Since April, French police have been conducting more frequent patrols of trains coming from Italy.

Earlier Tuesday, Italian police in riot gear forcibly cleared out a few dozen migrants who had been camping out for five days in Ventimiglia, a town on the border with France, after they had been pushed back by French police.

Under EU rules, migrants should be fingerprinted and registered in the first EU country in which they set foot. But in recent months Italy has allowed migrants who journeyed via the Mediterranean to slip into France, Austria and Switzerland without registering them first.

Tens of thousands of migrants have made the desperate voyage on all manner of vessels to cross the Mediterranean and enter Europe, often winding up in Italy.

At a joint news conference Tuesday, French Interior Minister Bernard Cazeneuve presented his Italian counterpart, Angelino Alfano, and the German minister, Thomas de Maizière, as “three friends confronted with a difficult problem they are trying to solve together.”

Mr. Cazeneuve said the situation in Ventimiglia was “difficult” for both Italy and France. “It is not France versus Italy or Italy versus France [and] not understanding each other. There is willingness to work together and our administrations work every day together, applying the rules of the European Union.

“We spoke frankly on this with Angelino and things are progressing on all these issues in a positive manner,” Mr. Cazaneuve added.

Mr. Alfano also sounded conciliatory. “We want to enhance cooperation with French police so events like [the push-backs] don’t happen again,” he said. “Meanwhile Europe is working on a relocation mechanism.”

Their statements were a change from earlier in the day, when the French and German ministers jointly told reporters that Italy needs to stick to its “responsibility” of registering all migrants arriving in its territory if it wants to help from EU-wide redistribution plans.

Speaking separately on his way into the meeting, Mr. Alfano said the scenes from Ventimiglia were a “slap in the eyes of those who don’t want to see that migrants want to go further north, not stay in Italy.”

France and Italy, as well as neighboring Austria and Switzerland, are part of the border-free Schengen area, which has done away with passport checks in 26 European countries.

But governments can still order police to check people’s travel documents 20 kilometers (12.4 miles) from the border, as long as the checks are “not systematic.” Border checks can also be temporarily reintroduced in cases of national security, such as terror attacks or big international events.

Germany, Europe’s top recipient of asylum seekers, had a stake in seeing an end to the Franco-Italian spat, and getting both governments on the same page regarding plans to redistribute immigrants throughout the EU.

The plan, put forward by the European Commission, the EU’s executive, would have 40,000 Syrians and Eritreans taken from Italy and Greece and sent to 23 other EU countries.

During a three-hour discussion on Tuesday, EU ministers still disagreed on whether the plan should be binding or voluntary. Poland, the Czech Republic, Slovakia, Hungary and the Baltic states are still against anything mandatory. Discussions among diplomats over the proposal have become heated in recent weeks.

“But for the first time we had the easterners speak in favorable terms, as long as there would be voluntary contributions to the plan,” Mr. de Maizière said.

A compromise could be found next week when EU leaders meet in Brussels to seek agreement on the “principle” of burden sharing, to be followed by working out details later in July, said Luxembourg Foreign Minister Jean Asselborn, whose country will chair the rotating EU presidency beginning July 1.