The Islamic State-inspired killer of a French police commander streamed his attack live on Facebook, according to a source close to the investigation.

French authorities said Larossi Abballa stabbed 42-year-old Jean-Baptiste Salvaing to death in front of his wife and their three-year-old son outside their home in Magnanville, north west of Paris, on Monday night (13 June).

The 25-year-old reportedly went on to take the officer's wife, Jessica, and son hostage, before posting a 13-minute live video on Facebook in which he swore allegiance to Islamic State (Isis) and considered what to do with the young child.

"I still don't know yet what I'm going to do with him," the killer is reportedly heard saying in the chilling video, as the child sat behind him on the sofa.

He went on to say his actions were prompted by a call from senior IS leader Abu Mohammed al-Adnani for followers in Europe and the United States to carry out attacks during Ramadan.

He also posted about 15 photos on Facebook using two accounts which have now been closed down, French security expert David Thomson told a Paris radio station.

A three-hour standoff with police, which culminated in a series of loud explosions and gunfire, saw him shot dead by French Raid commandos at about midnight local time. The authorities said the couple's toddler was "in shock but unharmed" and was receiving medical attention. The wife, a 36-year-old police secretary, was found dead inside with a knife wound to the neck.

The motive behind the attack – which began at around 9pm local time – is not yet clear. A news agency affiliated with IS claimed the double murder was carried out by an "Islamic State fighter".

A Facebook account said to belong to the attacker saw a post announce his "success" in killing a police officer and his wife at their home. He also claimed "the brothers in Sham [Isis territories]" are in contact with him.

Thomson said Abballa had called for the murders of police, prison officers and journalists – often by name – on social media before.

It also emerged Abballa, who grew up in nearby Mantes-la-Jolie, had previously been convicted for being part of a jihadist organisation with links to Pakistan.

He was sentenced to three years in jail in 2013, with six months suspended. Prosecutors claimed the organisation he was part of aimed to "prepare terrorist acts".

French President Francois Hollande said the attack was "unquestionably a terrorist act". Two other people said to be linked to Abballa were arrested on Tuesday morning.

Interior Minister Bernard Cazeneuve told reporters: "An appalling terrorist act was committed yesterday in Magnanville by an individual who attacked a police officer and his wife, who was herself an official in a police station."

IS claimed responsibility for previous attacks across Paris that left 130 people dead in November 2015.

Earlier in May, the US warned the Euro 2016 tournament which is taking place throughout France this month could be a target for terror attacks, with IS threatening to attack fans.