Obama said it was the first democratic election run by Afghans in more than three decades. The 2004 election that put President Hamid Karzai in power was run by the United Nations. Karzai and top challenger Abdullah Abdullah each described himself Friday as the likely winner of Thursday’s voting, although many believed they would be forced to compete in a runoff election in October.

The United States has been steadily increasing its military efforts in Afghanistan since Obama took office, arguing that that is a far more effective use of American troops than the Bush administration’s emphasis on the war in Iraq.

Obama said it was obvious in advance of the election that the Taliban, who control substantial portions of the country, particularly in the volatile south, would attempt to disrupt the voting.

“Over the last few days, in particular yesterday, we’ve seen acts of violence and intimidation by the Taliban, and there may be more in the days to come,” he said.

Regardless of the ultimate winner of the presidential election, the U.S. will continue to work with Afghans to stabilize the country, Obama said.

“Our goal is clear: to disrupt, dismantle and defeat al-Qaida and their extremist allies,” he said. “That goal will be achieved, and our troops will be able to come home as Afghans continue to strengthen their own capacity and take responsibility for their own future.”

With memories of the Sept. 11, 2001, terrorist attacks dimming, Americans are growing weary of the conflict. New polling this week showed a majority — 51 percent — of those surveyed now believe the war is not worth the fight, an increase of 6 percentage points in a month.

Still, a White House strategy review is due in mid-September, and Gen. Stanley McChrystal, the top U.S. commander in Afghanistan, is expected to press for a further increase in forces for his counterinsurgency campaign.

Just three years ago the U.S. had about 20,000 forces in the country. Today, it has triple that, on the way to 68,000 by year’s end when all of the extra 17,000 troops that Obama announced in March are to be in place. An additional 4,000 troops are arriving to help train Afghan forces.

Obama has not wavered from his campaign pledge to take the fight to the Taliban and their al-Qaida allies in Afghanistan and Pakistan. He argues that the true danger to Americans lies in the towering peaks and vast deserts of those countries, not in Iraq. The Bush administration, he asserts, wasted precious time, treasure and blood in toppling Saddam Hussein and getting caught up in an insurgency.

Independent U.S. analysts on Friday gave a generally upbeat assessment of the election process in Afghanistan.

“There’s no question that more of the polling stations were open than one had anticipated, given the threats and the violence from the Taliban,” said Mark Schneider, senior vice president of the International Crisis Group, which advises governments and international organizations.

James Dobbins, who was the Bush administration’s special envoy to Afghanistan in the early years of the war, said that from available information it appeared the election should be considered successful in the sense that it was a genuine political contest between viable candidates.

“The playing field was as level as one could reasonably expect under the circumstances,” said Dobbins, who is now director of international studies at the Rand Corp., a think tank.

Others cautioned not to overstate what the elections could do to advance political stability in Afghanistan.

“Just holding the election is an important sign — if not of progress, then at least of sustained effort toward that end state of a democratic Afghanistan,” said Daniel Markey, a Central Asia expert at the Council on Foreign Relations. “But in the near term, the best that we can hope is that they don’t prove to be even more disruptive and provide even more propaganda value to the insurgency.”