Fighting erupted in the western city of Herat on Sunday immediately after the assassination, which a spokesman for Governor Ismail Khan blamed on forces loyal to a senior government commander in the province, Zahir Nayebzada.
According to initial reports, at least 100 are said to have been killed in fighting after Sadiq's death.
"Unfortunately, he [Sadiq] has been killed," said local official Ghulam Muhammad Masoan. "He was in his car along with two police officers who were killed with him."
According to reports on state-run Kabul TV, Sadiq was killed along with three other people when a rocket-propelled grenade was fired on their vehicle.
Masoan blamed the killing on "a personal rivalry".
"Fighting is going on near the house of the commander," he said. "I cannot give you more details."
Troops loyal to Khan reportedly surrounded the home of senior military commander Nayebzada and a militia barracks in the city. Fighting broke out in several places, with several killed and injured, state TV said.
Aid workers in the city contacted by telephone reported shots ringing out on Sunday evening and said they had been ordered to hunker down.
Khan, a former anti-Soviet resistance commander who runs a large private army, has had firm control over Herat since the fall of the Taliban in late 2001.
President Karzai has struggled
to extend his writ beyond Kabul
But there have been persistent tensions and occasional factional fighting between his men and those loyal to rival commanders.
Nayebzada accused forces loyal to Khan of provoking the fighting by trying to take command of his division.
He said Khan's son was killed after breaking into his residence.
"[He] broke into my house and started the fighting there," Nayebzada said. "I did not kill Sadiq in an ambush. He was killed in a clash afterwards. More than 100 people have been killed on both sides.
Khan is said to be safe and in Kabul and had not been the subject of a second assassination attempt, contrary to earlier reports.
A spokesman for the governor, however, said Khan was in Herat.
Sadiq was the third member of President Hamid Karzai's cabinet to be assassinated, and the second civil aviation minister to die since Karzai's government came to power in place of the Taliban in late 2001.
In February 2002, Sadiq's predecessor, Abd al-Rahman, was assassinated at Kabul airport. Vice President and Public Works Minister Haji Abd Al-Qadir was shot dead at his office in July of that year.
In February last year, Minister for Petroleum and Mines Juma Muhammad Muhammadi died in an air crash off Pakistan.