Baghdad, Iraq (CNN) -- Saddam Hussein's cousin Ali Hassan al-Majeed -- also known as Chemical Ali -- was executed Monday, an Iraqi government spokesman said.

He was hanged after having been convicted on 13 counts of killings and genocide, Ali al-Dabagh said.

Al-Majeed had been sentenced to death in four separate trials, including one that focused on his involvement in a poison gas attack against Iraqi Kurds that killed about 5,000 people.

His execution had been delayed for political rather than legal reasons. It is not clear what change, if any, led to the reported execution.

Al-Majeed had been held in United States custody since his capture in 2003. But he was handed over to the Iraqi authorities in the 24 hours before his execution, U.S. Ambassador Christopher Hill told CNN's Diana Magnay on Monday.

The 1988 poison gas attack on the village of Halabja, which earned al-Majeed his nickname, was part of the Anfal campaign, in which the Hussein regime killed at least 100,000 Iraqi Kurds. The campaign is believed to be worst poison gas attack on civilians ever.

Al-Majeed was sentenced to death separately for his role in putting down a Shiite uprising against Hussein in 1991, and for his part in putting down a Baghdad revolt in 1999.

Estimates of the Shiite death toll in the 1991 rebellion range from 20,000 to 100,000. Al-Majeed was convicted of playing a key part in the slaughter during the revolt in southern Iraq that followed the 1991 Persian Gulf War.

One of his co-defendants in the Anfal case, Sultan Hashem, is a prominent Sunni leader who is considered a key player in efforts to reconcile the country's once-dominant Sunni community with the Shiite majority that now wields political power.

Hashem was also sentenced to death, but Iraq's Sunni Arab Vice-President Tariq al-Hashimi has long refused to sign his execution order. That delayed the execution of al-Majeed and another defendant as well.

Iraqi law requires all three members of the Iraqi presidency council -- the president and two vice-presidents -- to sign execution orders. It does not say what happens if they do not sign.

CNN's Yousif Bassil contributed to this report.