A news agency linked to IS said yesterday the attack had been carried out by an "Islamic State fighter", days after posting a similar claim following the massacre at a gay club in Orlando, Florida.
French prosecutors have launched an anti-terror probe after the policeman and his partner were killed at their home in the Paris suburb of Magnanville.
Witnesses told investigators the man stabbed the policeman repeatedly outside his home before holing up inside with the woman and the couple's three-year-old son.
"The anti-terror department of the Paris prosecution service is taking into account at this stage the mode of operation, the target and the comments made during negotiations with the RAID," one source said.
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The SITE Intelligence Group, a US-based monitor, cited the IS-linked Amaq News Agency as saying on its Telegram channels: "Islamic State fighter kills deputy chief of the police station in the city of Les Mureaux and his wife with blade weapons near #Paris."
The bloodshed also comes as France hosts the Euro 2016 football tournament under tight security -- still reeling from jihadist attacks in Paris last November that left 130 people dead.
The attacker was yet to be identified and neither of the victims was named, but the slain policeman was known to be 42 years old and worked in nearby Les Mureaux.
His partner was a local police official.
"A police commander and his partner, a civil servant at the interior ministry, were shamefully murdered this evening," Hollande said.
"All light will be shed on the circumstances of this terrible tragedy," he added, announcing a meeting of top officials at the presidential palace early today.
Officers found the woman's body when they stormed the house, and the attacker was killed during the assault, interior ministry spokesman Pierre-Henry Brandet said.