The cancellation of next weekend's runoff will be a huge relief to election officials, who were scrambling to hold the vote before the onset of Afghanistan's harsh winter, which was likely to close roads in the north and prevent voters from casting ballots.
Military officials also worried about security, days after a Taliban spokesman had threatened violence against anyone who took part.
Resolution of the election also has implications for U.S. strategy in the region. The Obama administration has said a credible Afghan partner is an essential element to U.S. success in Afghanistan.
Abdullah's withdrawal from the runoff election will not further complicate U.S. strategy in the region, senior White House advisor Valerie Jarrett told ABC News' George Stephanopoulos Sunday.
"It's up to the Afghan people and their authorities to decide how to proceed going forward," she said. "We watched the election very carefully. And 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."
Despite the cancelled runoff, Jarrett said, the president's long-awaited decision on Afghanistan could still slip to late November.
"The president will make a decision when he is confident he has all the facts he needs," she said on "This Week."
In the meantime, pressure on the president to decide whether to send more U.S. troops to the region is mounting.
Sen. Russ Feingold, D-Wis., member of the Foreign Relations Committee, issued a statement today saying the cancelled runoff is evidence that more troops in Afghanistan will be counterproductive.
"Increasing our military footprint will exacerbate the perception among Afghans that the U.S. intends to occupy their country in support of a government many see as illegitimate," Feingold said.
"This could further destabilize the situation in Afghanistan and Pakistan and make it more difficult to isolate and target al Qaeda globally, which is our top national security priority."
ABC News' Jake Tapper, Kirit Radia and Z. Byron Wolf contributed to this report.