France's President Emmanuel Macron and the Hungary's Prime Minister Viktor Orban vowed to "work together" despite political differences, after a meeting in Budapest in Monday.

As France is set to take over the presidency of the Council of the European Union in January, the Hungarian government invited Macron to participate in a meeting of the Visegrad group of which Slovakia, Poland and Czechia are part.

Macron has been critical of some of the countries in Eastern Europe, and of Orban in particular, in matters such as the rule of Law and LGBT+ rights.

Ahead of his visit, Macron said Paris and Budapest are "opponents" and during his visit to the Hungarian capital Macron sent a strong message to Orban by meeting several opposition leaders and visiting the grave of a well-known pro-democracy and anti-Orban activist.

On Monday, the Orban addressed Macron's comments lightly and offered a conciliatory approach, saying: "France is the home of encyclopedists, they are the best when it comes to definitions, so we accept their definitions: what we heard lately from Mr President is that we are political opponents and at the same time European partners."

During a joint press conference, Macron also expressed his will to cooperate further.

"We have political disagreements, which are well known, but we have the willingness to work together for Europe and to be loyal partners," Macron said.

Both leaders agreed on making the European Union more autonomous in terms of nuclear energy, farming and defense.

The migrant crisis is also a main topic of concern not only for France and Hungary but also the remaining Visegrad countries, which held an extraordinary meeting at the end of November on the situation in the Poland-Belarus border.

Warsaw has accused Belarus President Alexander Lukashenko of driving the rise in people trying to enter the EU through poland – a crisis that has spilled all the way over to French shores, where dozens of people have died trying to cross the Channel to the UK.

Since then, Macron has repeatedly argued for stronger control of the EU's external borders, which Hungary has supported in the past. However, the two nations have been at odds over the EU's migration and asylum-seeking laws, which Orban is accused of violating on several occasions.

"I also hope we will be able to find common ground on migration policy. There, too, we have had tensions in the past," Macron said.

"I think that what Europe has lived through the past weeks … is a reason for us to rethink our common organization, to better prevent migrant influxes, protect our external borders and find ways to cooperate more efficiently among Europeans on that matter," the French president added.