The death came as US Secretary of State Condoleezza Rice paid a surprise
visit to the country.
"The leader of the resistance died on Friday, November 11 at 2.20am," said a statement reputedly signed by the command of the dissolved former ruling Baath party.
There was a $US10 million ($A13.72 million) bounty outstanding on Ibrahim, 63, who was said to be gravely ill with leukaemia. He was erroneously reported to have been captured in September 2004.
Ibrahim was the most senior former Iraqi leader still at large since Saddam was captured in December 2003.
Born in Tikrit, the former Iraqi leader's home town, Ibrahim was considered to have been Saddam Hussein's daily right-hand man.
He was deputy commander-in-chief of the armed forces, and held a senior post on the committee responsible for northern Iraq when chemical weapons were used in 1988, killing thousands of Kurds.
There was no independent confirmation of the death, but 60 people gathered in his home town of Dur outside the former Baath party headquarters after television stations announced the news.
"To continue the Jihad (holy war), the Baath party regional command has decided to hand over responsibility for leading the resistance factions in Iraq to Abdul Kader Talab al-Duri, deputy to the secretary general of the party," the statement said.
Rice appeal
The death report came the day US Secretary of State, Condoleezza Rice, visited Iraq to encourage participation in next month's general elections.
In a televised press conference, she also appealed to Arab nations to condemn terrorism and establish diplomatic relations with Iraq.
"There are many embassies and ambassadors here, but not enough
from the Arab world," she said.
Other violence
As if in defiance, gunmen opened fire on the Omani Embassy less than two hours later in a drive-by shooting, killing a Sudanese employee and an Iraqi police guard.
Two more policemen, another Sudanese employee and an Iraqi civilian were wounded, an interior ministry official said.
Al-Qaeda in Iraq, controlled by Abu Musab al-Zarqawi, has repeatedly warned diplomats, especially those from Arab and Islamic countries, to stay away.
The group also announced it had kidnapped five Iraqi soldiers and seven foreigners, including Sudanese and Somalis, working as contractors for US forces following clashes in the western town of Hit.
In other violence, the US military announced the death of five servicemen.
Three died from wounds sustained in fighting, and two died in a road accident. That brought to 2,060 the overall number of US military casualties since the March 2003 invasion.
Three policemen also died and two were wounded when rebels machine-gunned their checkpoint in Baquba north of Baghdad, and seven people were wounded when a car bomb blew up in central Baghdad.