United States president George W Bush on Thursday demanded that those who were behind the 'cowardly' killing of former Pakistan prime minister Benazir Bhutto must be brought to justice.

Strongly condemning the assassination, a visibly tense Bush also urged the people of Pakistan to honour Bhutto's memory by continuing with the democratic process.

"The United States strongly condemns this cowardly act by murderous extremists who are trying to undermine Pakistan's democracy," Bhutto said.

"Those who committed this crime must be brought to justice," Bush said while reading out a brief prepared statement to reporters at a hangar near his Crawford ranch in Texas. He took no questions.

"Mrs. Bhutto served her nation twice as prime minister and she knew that her return to Pakistan earlier this year put her life at risk. Yet she refused to allow assassins to dictate the course of her country," Bush said in a statement released by the White House.

"We stand with the people of Pakistan in their struggle against the forces of terror and extremism. We urge them to honour Benazir Bhutto's memory by continuing with the democratic process for which she so bravely gave her life," he added.

"Laura and I extend our deepest condolences to the family of Benazir Bhutto, to her friends, to her supporters. We send our condolences to the families of the others who were killed in today's violence. And we send our condolences to all the people of Pakistan on this tragic occasion," he said.