He says the Afghan people are taking full responsibility for their country as the United States and its allies gradually withdraw their forces.
Obama is congratulating the millions of Afghans who defied threats from the Taliban and went to the polls.
Turnout in some places Saturday was so high that polling places ran out of ballots.
Partial results are expected Sunday.
Obama says the election to choose a successor to President Hamid Karzai (HAH'-mihd KAHR'-zeye) is critical to securing Afghanistan's democratic future and continued international support.