The Islamic State in Iraq said the killing of Abu Risha was a "heroic operation", but the authenticity of the statement could not be verified.
"Allah enabled your brothers ... to track down and assassinate the imam of infidelity and apostasy ... one of the dogs of Bush," said the statement.
Thousands of people gathered in Ramadi on Friday to attend Abu Risha's funeral.
"We blame al-Qaeda and we are going to continue our fight and avenge his death," Sheikh Ahmed Abu Risha, brother of Abdul Sattar Abu Risha, said on Friday.
Ahmed Abu Risha was elected the new leader of the Anbar Salvation Conference just hours after his brother's killing.
Pallbearers carried Abdul Sattar Abu Risha's body from Ramadi to the cemetery 10km outside the city, while the funeral procession shouted "revenge, revenge on al-Qaeda."
Others mourners chanted "there is no God but Allah and al-Qaeda is the enemy of Allah" and "Abdul Sattar is the pride of Ramadi".
Nuri al-Maliki, the Iraqi prime minister, was represented by Muwaffaq al-Rubaie, his national security adviser, who condemned the killing.
"It is a national Iraqi disaster. What Abu Risha did for Iraq, no single man has done in the country's history," al-Rubaie told the mourners gathered in the sheikh's house.
"We will support Anbar much more than before. Abu Risha is a national hero."
"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 [the US president]," Al Jazeera's James Bays said.
Abdul Sattar Abu Risha had urged the tribal leaders in other Iraqi provinces to follow 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, Anbar security chief, said.
"His car was hit directly."
No group immediately claimed responsibility for the bombing.
Sheikh Jubeir Rashid, a senior member of Abdul Sattar 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 Abdul Sattar 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. Anbar success
"Iraq is still under foreign occupation and Iraqis continue to die in great numbers"
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General David Petraeus, the senior US commander in Iraq, repeatedly pointed to successes in tackling a-Qaeda in Anbar during his testimony before the US congress.
Omar Abdul Sattar from the Islamic Party of Iraq told Al Jazeera that Abdul Sattar Abu Rishar had become a national symbol of the "national war against al-Qaeda".
"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 Abdul Sattar 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.
Bush mentioned the killing in a speech on Thursday in which he announced that he may pull some 30,000 US troops out of Iraq by mid-2008 effectively ending the so-called surge.
Hoda Abdel Hamid, Al Jazeera's Iraq correspondent, said Abdul Sattar Abu Risha's death could derail some of the US successes.
"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 Abdul Sattar Abu Risha's death, some Islamist websites posted messages praising his 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".