"A drone targeted the logistical support headquarters of Hashed al-Shaabi," mainly pro-Iranian former paramilitary units integrated into the Iraqi armed forces, said the security official.
The strike killed "two members and wounded seven others", said the official, speaking on condition of anonymity.
A Hashed source, also asking not to be named, confirmed the death toll and charged that the United States was behind the attack.
Harakat al-Nujaba, one of the Hashed's factions, said in a statement that "the deputy commander of operations for Baghdad, Mushtaq Talib al-Saidi" had been "martyred in a US strike".
It came amid heightened regional tensions since war broke out between US ally Israel and Iran-backed Hamas militants in the Gaza Strip, triggered by the Palestinian group's deadly October 7 attack.
There was no immediate comment from US officials, whose forces in Iraq and neighbouring Syria have faced a surge in attacks since the start of the Israel-Hamas war.
Videos shared on a Telegram channel linked to the Hashed showed columns of smoke rising above the area of the strike on Baghdad's Palestine street, normally a bustling commercial road.
Washington has counted more than 100 attacks against US targets in Syria and Iraq since mid-October.
Many have been claimed by the Islamic Resistance in Iraq, a loose alliance of Iran-linked armed groups that oppose US support for Israel in the Gaza war.
The United States has around 2,500 troops in Iraq and 900 in Syria as part of a multinational coalition fighting the Islamic State group.
The US military has responded to recent attacks by launching air strikes targeting sites used by Iran and its proxy forces in Iraq and Syria, including Hashed sites.
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