The Belgian Police arrested three people on Saturday in raids in a poor, immigrant quarter of Brussels as they pursued emerging links between the Paris attacks and an Islamist bastion in France's northern neighbour.

Prime Minister Charles Michel said at least one of those held from the inner Brussels neighbourhood of Molenbeek was believed to have spent the previous evening in Paris, where two cars registered in Belgium were impounded close to scenes of some of the violence, including the Bataclan music hall.

"Police operations will go on," Michel told RTL television after late-night police raids in Molenbeek, west of the city centre, which is home to many Muslims, notably families originally from Morocco and Turkey. His interior minister spoke impatiently of going in to "clean up" Molenbeek.

"We're talking about a network," said the borough's mayor Francoise Schepmans on Sunday, referring to a total of five arrests in Molenbeek.

A French prosecutor said a car hired in Belgium was linked to the attacks and that a Frenchman living in Brussels rented it and was later stopped early on Saturday at the Belgian border.

A parking ticket issued in Molenbeek was found in the hire car in Paris. Officials declined comment on reports that the attacks may have been largely plotted in Brussels, that one of three attack teams came from there and that at least three of the attackers were based in the European Union capital.

Proportional to its 11 million population, of whom half a million are Muslim, Belgium has been the European country which has contributed the most foreign fighters to the civil war in Syria -- over 300 by official estimates a year ago -- and it has figured in many Islamist attacks and plots across the continent.

Many international security experts have long seen Belgium, with its Muslim population, fragmented state structures resulting from bitter divisions between French- and Dutch-speakers and a history as a market for firearms, both legal and illegal, as an "Achilles heel" of violence Islam across Europe.

A prominent Moroccan-born member of the group behind the 2004 Madrid train bombings that killed 191 was from Molenbeek.

The area has been connected with two attacks in France this year. Security officials have said the Islamist who killed people at a Paris kosher grocery in January at the time of the attack on the magazine Charlie Hebdo acquired weapons in the district. So too did the man overpowered in August on a Thalys high-speed train from Brussels to Paris before he killed anyone.

An alleged plot to attack Belgian police in January, which was broken up by raids in which two men were killed in the eastern town of Verviers, had connections to Molenbeek. And a Frenchman accused of shooting dead four people last year at the Jewish Museum in Brussels also spent time in the area.