The withdrawal by Afghan President Hamid Karzai's chief rival from a runoff election shouldn't complicate President Barack Obama's decision on whether to send more troops to that country, senior White House aides said.

Abdullah Abdullah on Sunday said he would not participate in Afghanistan's Nov. 7 runoff, after failing to reach an agreement with Mr. Karzai on how to redress problems with fraud that had marred the presidential election in August.

His announcement comes as Mr. Obama has been weighing a request from Gen. Stanley McChrystal, the top U.S. commander in Afghanistan, for at least 40,000 more troops to help fight the extremist Taliban and prevent al Qaeda from reestablishing a base in the country. Senior administration officials have frequently cited the need for a reliable "partner" in Kabul as a central part of its Afghan war strategy, and the administration is expected to wait until after the runoff to announce its new troop plans.

Asked whether Dr. Abdullah's withdrawal would delay Mr. Obama's decision, senior White House adviser David Axelrod told CBS's "Face the Nation" on Sunday that "Abdullah Abdullah made a political decision to withdraw. That doesn't markedly change the situation." He suggested that the president could make a decision on troops in a matter of weeks.

Some 68,000 American troops will be based in Afghanistan by the end of the year.

Mr. Axelrod said that while Dr. Abdullah had established himself as the leader of the country's opposition, polls suggested that he was likely to be defeated in a runoff. "We'll just deal with the government that's in," Mr. Axelrod said.

Another senior Obama aide, Valerie Jarrett, said on ABC News's "This Week" that Dr. Abdullah's decision should not add a complication to the administration's Afghanistan strategy.

"It's up to the Afghan people and their authorities to decide how to proceed going forward," she said. "We're going to work with the leader of the Afghan government and hopefully that's going to improve the state of conditions for the people in Afghanistan, and also help us, as we try to bring this war to a close."

The aides reiterated that Mr. Obama wanted to ensure that the U.S. had a sound Afghanistan strategy, with the goal of preventing a return by al Qaeda to that country, before making a decision on troops.

House Minority Leader John Boehner, appearing on CNN's "State of the Union," said President Karzai has been widely expected to be reelected, so Dr. Abdullah's exit from the race "should not hamper our decision with regard to Afghanistan." He urged Mr. Obama to make a decision quickly.

"The longer this decision hangs, the more jeopardy and the more danger our troops on the ground there are in the middle of," Mr. Boehner (R., Ohio) said. "We've had the highest casualty totals in years over the last month or two. Why? Because all of the uncertainty around what the president's going to decide."

Sen. Joseph Lieberman, an independent from Connecticut, told "Face the Nation" that it was important to "keep our eye on the ball here," and that the reason that the U.S. was in Afghanistan was to stop the Taliban and an Al Qaeda from coming back into control.

"Everyone knows the Karzai government can be improved, but look, Hamid Karzai is going to be the next president of Afghanistan," Mr. Lieberman said. "I think it's time for us to stop beating up on President Karzai and start building up President Karzai and his government to be the government we need. Because they're not the enemy. The enemy is the Taliban….It's time to send help."

Write to Kathy Chen at