Turnout was 7 million out of 12 million eligible voters, or about 58 percent, according to preliminary estimates in what will bring the first-ever democratic transfer of power in a country plagued by conflict.
"We commend the Afghan people, security forces, and elections officials on the turnout for today's vote - which is in keeping with the spirited and positive debate among candidates and their supporters in the run-up to the election," Obama said in a statement.
The United States has been at odds with Afghanistan President Hamid Karzai who has refused U.S. entreaties to sign a bilateral security agreement that would permit about 8,000 U.S. troops to remain in the country after the formal American withdrawal at the end of this year.
U.S. officials are keeping open the option of leaving behind a troop contingent for training Afghan forces and for a counter-terrorism mission if an agreement can be signed later this year by Karzai's successor.
"These elections are critical to securing Afghanistan's democratic future, as well as continued international support, and we look to the Afghan electoral bodies to carry out their duties in the coming weeks to adjudicate the results - knowing that the most critical voices on the outcome are those of Afghans themselves," Obama said.
Obama paid tribute to the sacrifice of American forces who have served in Afghanistan since the Sept. 11, 2001, attacks.
"The United States continues to support a sovereign, stable, unified, and democratic Afghanistan, and we look forward to continuing our partnership with the new government chosen by the Afghan people on the basis of mutual respect and mutual accountability," he said.