In May, Prime Minister Mustafa al-Kadhimi ordered federal security forces to arrest Mr. Muslih.
Mr. Muslih, a Karbala native, is the leader of Al Tafuf Brigade, an Iran-backed militia in Anbar Province in western Iraq. The Muslih and al-Wazni families lived in the same Karbala neighborhood for years.
His arrest in May set off an armed showdown with the paramilitary groups.
The prime minister, who had taken office in 2019 promising to bring the militias to heel, agreed to hand Mr. Muslih over to the paramilitary command, which released him after a judge said there was insufficient evidence to charge him. An arrest warrant was also issued for Ali Muslih. (The two brothers declined to be interviewed for this article.)
Mr. Muslih lived in Iran for almost a decade. After the killing of Mr. al-Wazni, demonstrators burned barricades around the Iranian consulate in Karbala in protest.
In normal times, at least one million Shiite pilgrims a week come to Karbala to visit the shrines of Imam Hussein and Imam Abbas, who are at the heart of Shiite identity. Most of the visitors are from Iran.
Even during the pandemic, the shrines, with their marble courtyards and dazzling mirror mosaics topping Iranian ceramic tiles, are packed with pilgrims. On sweltering summer days, fans with water reservoirs spray the tourists with a fine mist as they shop for religious keepsakes made from Karbala’s clay.