In video, Coulibaly says he coordinated attacks with Chérif and Saïd Kouachi, but it is clear they followed different factions

The gunman who killed four people in a Parisian kosher grocery store and a policewoman pledged allegiance to Islamic State in a video published online on Sunday, two days after his death.

In the seven-minute video, Amedy Coulibaly is described as a “soldier of the caliphate” and is filmed declaring allegiance to the Isis leader, Abu Bakr al-Baghdadi.

Coulibaly shot dead a Parisian policewoman on Thursday and four hostages at a kosher supermarket on Friday. French police said on Sunday that he had also shot and injured a jogger on Wednesday in the Paris suburb of Fontenay-aux-Roses, at the onset of a wave of attacks that have shaken Europe. The jogger was seriously wounded by a bullet from the same Tokarev gun that Coulibaly carried when he stormed the supermarket two days later.

In the video, Coulibaly said he had coordinated his attacks with Chérif and Saïd Kouachi, the brothers who stormed the offices of Charlie Hebdo in Paris on Wednesday, killing 12 people.

“We did some things together, some things separate – that way we would have more of an impact … we arranged it to synchronise [our movements] so we would go out at the same time, which was not a problem,” he said.

Facebook Twitter Pinterest Watch excerpts from the video

Coulibaly and the Kouachi brothers died within minutes of each other in separate shootouts with the police at the supermarket and at a printworks east of Paris. But it is clear they drew their inspirations from different jihadist factions.

The Kouachis declared themselves followers of al-Qaida in the Arabian Peninsula (AQAP), and it emerged on Sunday that they had both gone to Yemen for weapons training in 2011.

“These two brothers arrived in Oman on 25 July 2011, and from Oman they were smuggled into Yemen, where they stayed for two weeks,” a senior Yemeni security official told Reuters.

The official, who was not named, said the brothers met the US-born AQAP preacher Anwar al-Awlaki a few months before he was killed in a US drone strike in Yemen in September that year.

The Kouachis “were trained for three days in the deserts of Marib on how to fire a gun. They returned to Oman and they left Oman on 15 August 2011 to go back to France,” the official said.

The Yemeni AQAP link is likely to raise more questions over the decision of the French domestic security service, the DGSI, to drop surveillance of the Kouachi brothers months before the Charlie Hebdo attacks.

DGSI phone surveillance on Chérif Kouachi was suspended at the end of 2013, and on Saïd in the summer 2014, according to the Libération newspaper.

“Wiretap warrants were not renewed because there were other priorities and Chérif, at that time, seemed to be moving in the direction of peddling fake goods. He wasn’t really in touch with the most dangerous people in radical Islamic circles,” a French government source told Libération.

It is not clear why surveillance was lifted on Saïd Kouachi last summer. L’Express newspaper reported that the police focus shifted to “other suspects”.

Coulibaly’s wife, Hayat Boumeddiene, was reported to have slipped through the net cast by the French security forces. She is reported to have flown to Turkey before the attacks, on 2 January, disappearing without trace close to the Syrian border.

It emerged that she had been in near-constant touch with Chérif Kouachi’s wife, talking to her more than 500 times by phone over the course of 2014. Pictures have surfaced on the web of Boumeddiene, 26, shrouded in a black niqab, practising firing a crossbow and posing with her husband.

The worldwide investigation triggered by the Paris killings will focus most urgently on the possibility that they mark the start of a campaign and that there are other cells of jihadists planning similar assaults across Europe and beyond. Isis statements on Sunday claimed that Paris was the first blow in a wave of attacks.

However, it is far from clear whether Isis or AQAP played any operational role in the attacks or merely supplied the inspiration and then attempted to stamp their brand on the killings. For both organisations, the international outrage sparked by the murders represents valued publicity.

Isis has up to now been only a regional actor in Syria and Iraq. The video showing Coulibaly swearing allegiance gives the group the appearance of a global force.

For its part, AQAP had proved one of the most potent al-Qaida affiliates in terms of its ability to carry out operations against western targets, but in the past few years since the killing of Awlaki it had appeared to be withering and conducting fewer attacks outside Yemen.

The Charlie Hebdo killings suggest that Awlaki, whose video tirades are still circulated in jihadist circles, continues to have an influence.

According to Yemeni reports, Saïd Kouachi shared a room at some point in the capital, Sana’a, with Umar Farouk AbdulMutallab, a Nigerian AQAP member who was arrested in Detroit in December 2009 for an abortive attempt to blow up a civilian airliner with explosives hidden in his underwear. AbdulMutallab, 23 at the time, had previously studied engineering in London.

Isis and al-Qaida have been fierce rivals in Middle East extremist politics since Isis broke away from al-Qaida last year, but the Paris attacks have shown that such distinctions are blurred among young jihadis in the west looking for inspiration.

French prisons appear to have acted as a melting pot and indoctrination centre for the country’s alienated young, particularly from immigrant communities. Coulibaly met Chérif Kouachi in jail, when Coulibaly was serving time for armed robbery and Kouachi for his role in a jihadist recruiting network centred on, and named for, the Buttes Chaumont park in Paris, where recruits did their training.

It was reported on Sunday that the ideologue of the group, Farid Benyettou, who was sentenced to six years in prison in 2008, had been working since December as a trainee nurse at a Paris hospital. According to Le Parisien newspaper, Benyettou was not at work on Wednesday or Thursday but was on duty over the weekend in the same hospital where some of the casualties from the Charlie Hebdo attacks had been taken. The hotel authorities denied he had any contact with the victims.

While in jail both Coulibaly and Kouachi met Djamel Beghal, a French-Algerian al-Qaida recruiter convicted for a 2001 attempted attack on the US embassy in Paris.

Both men appear to have emerged from prison as committed jihadis. Soon after being freed in 2010 they were arrested again, this time for a plot to free an Algerian terrorist sentenced for bomb attacks in 1995 on the Paris metro. Coulibaly was sentenced to five years while Kouachi was eventually freed for lack of evidence of his involvement.

Both were part of an active jihadist culture in Paris and were well known to the authorities. Part of the investigation now gathering momentum will focus on how the intelligence agencies and police took their eye off the young Parisians who carried last week’s attacks.

Another, more pressing, aspect of the inquiry will be an attempt to ascertain how many more European jihadis like the Kouachis, Coulibaly and Boumeddiene are still out there, waiting for their moment.