They are being held over a corruption investigation, it adds.

A fifth top industrialist, Issad Rebrab, on Twitter denied reports he had also been arrested, saying he went to the police on a business matter.

Mr Bouteflika, who had been in power for 20 years, resigned three weeks ago following anti-government protests.

Fresh elections are expected in July.

The four brothers are from the Kouinef family, named as Reda, Tarek, Abdel Kader and Karim.

They were detained in Algiers on Sunday as part of an investigation into non-compliance with state contracts.

The brothers are involved in a range of business activity, including civil engineering.

There was no immediate statement from the brothers.

Issad Rebrab is the head of the Algerian conglomerate Cevital

Their detention comes after the head of the army, Lt Gen Gaïd Salah said last week that some among the ruling elite could be questioned over alleged corruption, Reuters news agency reports.

Protesters who had been demanding the resignation of Mr Bouteflika, had also been calling for the downfall of "Le Pouvoir", or the establishment, meaning that all those around the former president should also go.