A man wielding a knife went on the rampage in a park south of Paris, killing a man out for a walk with his wife and wounding two other people before being shot dead by police, officials said.

The Paris police department said the man had attacked "several people" around lunchtime in the park in the suburb of Villejuif.

Some managed to evade him, but the man claimed at least one life, that of a 56-year-old Villejuif local, according to the commune's mayor Franck Le Bohellec.

The victim "was walking with his wife when the attacker approached; he wanted to protect his wife" and was stabbed, the mayor explained.

According to a source close to the inquiry, another man was seriously wounded in the attack and a woman sustained light injuries.

According to Laure Beccuau, prosecutor of the Cretail commune southeast of Paris, the man had tried to stab others, but "they managed to evade him."

The assailant fled the park to the neighbouring suburb of Hay-les-Roses, where he was later shot dead by police.

He had made his way to a shopping centre "where he seemingly intended to continue his attack," Hay-les-Roses mayor Vincent Jeanbrun told BFMTV.

"Luckily the police were quickly alerted and made their way rapidly to the scene where they neutralised him by killing him," Mr Jeanbrun said.

Laurent Nunez, number two at the interior ministry, said the police had interrupted "a killing spree".

Interior Minister Christophe Castaner in a tweet thanked the police for "reactivity, composure and professionalism."

The police have opened an investigation of murder and attempted murder.

In the past four years, the French capital has been rocked by major attacks resulting in mass casualties.

In October last year, four people were stabbed to death at the Paris police headquarters by Mickael Harpon, an IT specialist working for the police.

Prosecutors said that attacker, who was shot dead by police, had come under the sway of radical Islamists.

Coordinated bombings and shootings by Islamist militants in November 2015 at the Bataclan theatre and other locations around Paris killed 130 people in the deadliest attacks in France since World War Two.