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The Americans blame him for co-ordinating some of the attacks on US-led forces and have offered a $10m reward for his capture.
Mr Douri was one of the key plotters who carried out the coup that brought the Baath Party to power in 1968.
In later years he served as the Iraqi leader's number two in the powerful Revolution Command Council, as vice-chairman.
| If you have forgotten Halabja, we are ready to repeat the operation Izzat Ibrahim to the Kurds, reminding them of chemical attacks they suffered |
US officials call Mr Douri the "single most significant regime figure" still on the loose in Iraq.
They hope the net is tightening around the man known as Saddam Hussein's enforcer.
Four of his nephews were captured on 14 January. His wife and daughter are still in US custody after being arrested last November.
Mr Douri 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.
War crimes charges have been issued against him in Austria.
Ruthless
When the Gulf War broke out in 1991, The New York Times newspaper quoted him as warning the Kurds not to cause trouble.
He reminded them of the chemical attack with the words: "If you have forgotten Halabja, I would like to remind you that we are ready to repeat the operation."
Mr Douri was born the son of an ice seller in 1942 near Tikrit, where Saddam Hussein had his power base.
He joined the Baath Party, rising swiftly through the ranks after the 1968 coup. In the 1970s, he served as both agriculture and interior minister.
Diagnosed with leukaemia several years ago, his subsequent recovery enabled him to pursue a challenging domestic and foreign work schedule.
He travelled abroad frequently as the Iraqi leader's envoy and was sent to woo neighbouring states during the pre-war stand-off with Washington.
Close shaves
At the 2002 Arab summit in Beirut, Mr Douri broke the ice by publicly shaking hands with the Kuwaiti foreign minister and embracing the Saudi crown prince.
Both countries had previously refused to have any direct dealings with Iraq. He pledged to respect Kuwait's "territorial integrity".
He chaired the Arab Parliamentary Union session in Baghdad in September 2002, calling for Arab solidarity in the face of the "American-Zionist threat".
He had some narrow shaves, escaping an assassination attempt in the city of Karbala in 1998, and avoiding arrest in Vienna in 1999 for suspected crimes against humanity while on a private visit for medical treatment.
Announcing that Saddam Hussein had won 100% approval in a 2002 referendum to give him another term as president, Mr Douri hailed "the great success of this unique democratic practice".
Mr Douri's daughter was briefly married to Saddam Hussein's elder son, Uday.