In a seven-minute, 16 second video released Sunday, Amedy Coulibaly, the Paris gunman who attacked a kosher supermarket on Jan. 9, pledges allegiance to the Islamic State and its leader Abu Bakr al-Baghdadi. The Post has edited and translated the video. (The Washington Post)

One of the assailants in the Paris terrorist attacks claimed in a posthumously released video that he was acting on behalf of the Islamic State, in coordination with the two brothers who attacked a satirical newspaper and said they were affiliated with al-Qaeda.

The video, released Sunday, features Amedy Coulibaly, the gunman who killed four hostages at a Paris supermarket Friday before he was slain by police. It pointed to the dangers, long anticipated by law enforcement, posed by the expanding allure of the group that has conquered vast areas of Iraq and Syria over the past two years, even as al-Qaeda continues to pursue its own agenda of staging attacks against the West.

The video offered no evidence, however, that Coulibaly had been in contact with the Islamic State before his assault on the supermarket, which may represent another example of the “lone wolf” attacks that the Islamic State has inspired, analysts said.

A fierce feud erupted last year between the Islamic State and its progenitor, al-Qaeda, and many analysts have speculated that the Paris attacks, claimed by al-Qaeda’s Yemen affiliate, al-Qaeda in the Arabian Peninsula, represented an attempt by the older group to reassert its relevance.

Coulibaly’s comments suggest that the feud has not deterred cooperation among friends on the ground, although it could not be confirmed that his claims of collaboration were real.

The video begins with footage of Coulibaly, 32, doing exercises, then switches to a scene in which he sits in front of a white sheet and pledges allegiance to the Islamic State and its leader, Abu Bakr al-Baghdadi.

Coulibaly cited the airstrikes carried out against the Islamic State by the U.S.-led coalition, in which France participates, as one of the motives for his assault on the supermarket, which came two days after two brothers, Said and Chérif Kouachi, stormed the offices of the French satirical newspaper Charlie Hebdo and killed 12 people.

“You attack the Islamic State. We attack you,” he said, speaking in French and occasionally lapsing into broken Arabic, in a segment of the recording that showed him wearing a leather jacket and wool cap, seated beside an AK-47 automatic rifle. “You and your coalition, so that you who are almost in the lead now, you bombard there regularly,” he said. “You kill civilians, you kill combatants, you kill.”

Other segments showed him wearing Arab and African robes and a flak vest, suggesting they were recorded at different times, though all appeared to have been filmed in the same place. The furnishings and stripped hardwood floors suggest an apartment in France.

At least one segment, which refers to the Charlie Hebdo attack, was likely recorded in the two days that elapsed between the attacks, and the video begins and ends with footage of police bursting into the supermarket and shooting Coulibaly.

The video lacked the sophisticated editing techniques typically associated with Islamic State videos, and French authorities have not indicated that Coulibaly was among the more than 700 French citizens who are thought to have traveled to Syria to fight.

The video was first posted by an obscure jihadist account on Twitter, rather than the Islamic State’s official forums, according to Aaron Zelin, an expert in jihadist movements at the Washington Institute for Near East Policy. That gives no reason to believe Coulibaly had been directed to act by the Islamic State, only that he was connected to a wider network of jihadists who sympathize, support and perhaps dispatch volunteers to fight for the organization, he said.

In the video, Coulibaly claimed he acted as part of a “team” with the brothers who attacked the offices of Charlie Hebdo and provided money to help them in their assault.

“We did some things together and others separately in order to have more impact,” he said. “I helped this project by giving them a few thousand euros.”

Said and Chérif Kouachi, who carried out the attacks against the newspaper, had earlier said they were acting on behalf of al-Qaeda in the Arabian Peninsula, and at least one of them had spent time in Yemen in 2011, according to French and U.S. officials. The al-Qaeda in the Arabian Peninsula group later claimed responsibility for their attack.

Coulibaly’s wife, Hayat Bou­meddiene, who is wanted by the French authorities, was reported by French and Turkish officials to have traveled to Turkey and then across the border into Syria in the days immediately preceding the attacks. She had participated in more than 500 telephone calls with the wife of Chérif Kouachi, one of the Charlie Hebdo attackers, suggesting the attackers all knew one another.

But that also demonstrates only that Coulibaly and Boumeddiene had contacts among jihadists, Zelin said. “Obviously he was coordinating with them, but maybe he was sort of doing his own thing at the same time,” he said.

The Twitter account that posted Coulibaly’s claim appeared to refer obliquely to an upcoming attack in a posting on Dec. 25. Referring to the Islamic State’s repeated calls for “lone wolf” attacks, the account says, “We have responded to the call. . . . and what is coming is worse and more bitter.”

According to French authorities and media reports, Coulibaly, whose parents came to France from the former French colony of Mali, had been radicalized in prison while serving a sentence for robbery from 2002 to 2007. There, he met Chérif Kouachi and also fell under the influence of Djamel Beghal, a preacher who was serving a 10-year sentence for plotting to attack the U.S. Embassy in Paris.

In 2010, he returned to prison again, for his part in an attempt to spring from jail Smaïn Ait Ali Belkacem, who had masterminded a series of terrorist attacks in Paris in 1995. Coulibaly was released in May.

Anthony Faiola and Griff Witte in Paris contributed to this report.