U.S. Secretary of State Hillary Rodham Clinton on Sunday urged the Afghanistan government to ensure the legitimacy of the presidential election process, following a key presidential challenger quit the election.

Accusing President Hamid Karzai of failing to meet his demands for a fair and transparent vote, presidential candidate Abdullah Abdullah said Sunday that he decided to quit the election, which is set on November 7.

According to Afghan constitution, it is possible for the runoff to be held with only one candidate, but that is believed to undermine the government's legitimacy.

"I recognize the decision by Dr Abdullah Abdullah not to participate in the second round of balloting in the Afghan presidential elections," Clinton, who has been visiting the Middle East, said in a statement.

"It is now a matter for the Afghan authorities to decide on a way ahead that brings this electoral process to a conclusion in line with the Afghan constitution," said Clinton, adding that the United States will support the next Afghanistan president.

Praising Abdullah of running "a dignified and constructive campaign" in the election, Clinton said Washington hopes Abdullah continue to "stay engaged in the national dialogue and work on behalf of the security and prosperity of the people."

Abdullah's pulling out of the election reportedly came after talks of forming coalition government between Karzai and Abdullah broke down on Saturday.

Abdullah presented some conditions to Karzai and his government one week ago to ensure the credibility of the runoff, including replacing top election official and suspending three ministers.

The first-round election was held on August 20, with preliminary results by Afghan election authority showing Karzai won 54.6 percent. However, a UN-backed investigation panel accused the election of widespread fraud and pushed Karzai's total to below the 50 percent, which is needed to avoid a runoff.

Earlier on Sunday, U.S. President Barack Obama's senior adviser David Axelrod told CBS television that Abdullah's quit will not " markedly change" the situation in Afghanistan.

"Every poll that has been taken there suggested that he (Abdullah) was likely to be defeated anyway," said Axelrod, adding "we are going to deal with the government that is there."

"Obviously there are issue we need to discuss, such as reducing the high level of corruption. These are issues we will take up with President Karzai," said Axelrod.

The Obama administration is weighing his strategy on Afghanistan and considering whether to send tens of thousands additional troops to the war-torn country while Taliban has vowed to disrupt the runoff election.