Al Qaeda’s offshoot in Yemen claimed responsibility for the attack on a Paris magazine by two French brothers, reasserting its dominance among terror organizations targeting the West.

The announcement on Wednesday came as French investigators said they are searching for another man whom they have identified as a suspect in last week’s attacks.

The assertion by al Qaeda in the Arabian Peninsula, or AQAP filled out the emerging picture of a long-standing relationship between Said and Chérif Kouachi and AQAP. It came amid new indications that the older brother, Said, was more deeply involved in militancy in Yemen than was previously known. A Yemeni security official disclosed for the first time that Said is believed to have trained at camps run by AQAP during the nearly two years he spent in Yemen.

Nasser bin Ali al-Ansi, a founding member of AQAP who is part of the group’s inner circle of leadership, claimed Anwar al-Awlaki, a senior AQAP operative, planned the magazine attack before his death in a U.S. airstrike in September 2011.

Mr. Ansi said the group’s leadership “chose the target, laid the plan and financed the operation.”