"This is a man who has had a controversial past, but in recent months he has become a very prominent figure, even meeting George Bush," Al Jazeera's James Bays said.
Abu Risha had urged the tribal leaders in other Iraqi provinces to follow al-Anbar's lead in co-operating with the central government against al-Qaeda.
"He was returning home when his convoy was hit by a roadside bomb planted by insurgents," Colonel Tareq al-Dulaimi, al-Anbar security chief said.
"His car was hit directly."
No group immediately claimed responsibility for the bombing.
Sheikh Jubeir Rashid, a senior member of Abu Risha's group, told the Associated Press: "It is a major blow to the council, but we are determined to strike back and continue our work.
"Such an attack was expected, but it will not deter us."
Two of Abu Risha's bodyguards were also killed by the roadside bomb, Colonel Tareq Youssef, supervisor of Anbar police, said.
Police announced a state of emergency in Ramadi after the bombing and set up additional checkpoints throughout the city, Rashid said.
General David Petraeus, the senior US commander in Iraq, repeatedly pointed to successes in tackling al-Qaeda in al-Anbar province during his testimony before the US congress.
Omar Abdul Satar from the Islamic Party of Iraq told Al Jazeera Abu Rishar had become a national symbol of the "national war against al-Qaeda".
|"It is a major blow to the council, but we are determined to strike back and continue our work"|
Sheikh Jubeir Rashid, Anbar Salvation Council
"His programme now against al-Qaeda has become a national programme. Diyala province, Salahuddin province, Baghdad province are following now his programme," he said.
The White House condemned Abu Risha's "assassination".
"His death also reminds us that the struggle will require continued perseverance, and the Iraqis are increasingly turning away from al-Qaeda, as a result of such extreme acts of violence," Kate Starr, White House national security council spokeswoman, said.
During a 15-minute address to the nation on Thursday evening (0100 GMT on Friday), Bush is expected to announce that he may pull some 30,000 US troops out of Iraq by mid-2008 effectively ending the so-called "surge".
But Hoda Abdel Hamid, Al Jazeera's Iraq correspondent, said the killing could derail some of the US successes.
"Al-Anbar province was really the capital of al-Qaeda in Iraq ... he managed to convince the tribes to give up their young people to make up the police and armed forces in the province," she said.
Within hours of Abu Risha's death, some militant websites posted messages praising Abu Risha's killing, the Associated Press news agency reported.
One called him "one of the biggest pigs of the Crusaders," while another said he would spend Ramadan "in the pits of hell".