An investigation has been launched by French anti-terrorism prosecutors. (Photo: AFP)

A Sudanese refugee went on a knife rampage in a town in southeastern France on Saturday, killing two people in what is being treated as a terrorist attack.

The attack in broad daylight, which President Emmanuel Macron called "an odious act", took place with the country on lockdown in a bid to stem the spread of the deadly coronavirus.

Counter-terrorism prosecutors have launched an investigation into "murder linked to a terrorist enterprise" after the rampage in a string of shops in Romans-sur-Isere, a riverside town with a population of about 35,000.

The assailant, identified only as Abdallah A.-O., a refugee in his 30s from Sudan who lives in the town, was arrested without a fight by police.

"He was found on his knees on the pavement praying in Arabic," the prosecutor's office said.

According to witnesses cited by local radio station France Bleu Drome Ardeche, he shouted "Allah Akbar!"(God is Greatest) as he stabbed his victims.

"Anyone who had the misfortune to find themselves in his way were attacked," town mayor Marie-Helene Thoraval told AFP.

David Olivier Reverdy, from the National Police Alliance union, said the assailant had called on police to kill him when they came to arrest him.

- 'Jumped over the counter' -

The suspect first went into a tobacco shop where he attacked the owner and his wife, Thoraval said.

He then went into a butcher's shop where he seized another knife before heading to the town centre and attacking people in the street outside a bakery.

"He took a knife, jumped over the counter, and stabbed a customer, then ran away," the butcher's shop owner Ludovic Breyton told AFP.

"My wife tried to help the victim but in vain."

Interior Minister Cristophe Castaner, who visited the scene, said two people were killed and five others injured.

"This morning, a man embarked on a terrorist journey," he said.

The initial investigation has "brought to light a determined, murderous course likely to seriously disturb public order through intimidation or terror", according to the national anti-terrorism prosecutor's office (PNAT).

It said that during a search of the suspect's home, "handwritten documents with religious connotations were found in which the author complains in particular that he lives in a country of non-believers".

The suspect, who obtained refugee status in 2017, was not known to police or intelligence services in France or Europe, PNAT said.

Macron denounced the attack in a statement on Twitter.

"All the light will be shed on this odious act which casts a shadow over our country which has already been hit hard in recent weeks," he said.

France is in its third week of a national lockdown over COVID-19, with all but essential businesses ordered to shut and people told to stay at home.

The country has been on terror alert since a wave of deadly jihadist bombings and shootings in Paris in 2015.

In all, 258 people have been killed in France in what have been deemed terrorist attacks.