Saying that “the American people are encouraged by the progress that has been made,” Mr. Obama, standing next to Mr. Karzai at the heavily fortified presidential palace, added pointedly work remains to be done on the governance issues that have vexed American officials over the past year. “We also want to continue to make progress on the civilian process,” Mr. Obama said. He mentioned several areas, including anti-corruption and the rule of law.

The trip highlighted how far the administration believes that the Afghan government has to go to make good on promises that Mr. Karzai has made to the international community on governance and even reintegration with certain reconcilable members of the Taliban insurgency.

Gen. James L. Jones, the national security adviser, told reporters on Air Force One enroute to Afghanistan that the administration wanted Mr. Karzai to “understand that in his second term, there are certain things that have not been paid attention to, almost since day one.” General Jones said that the Afghan president “needs to be seized with how important” the issue of corruption, in particular, is for American officials.

The visit capped a high-profile week for Mr. Obama, one in which he achieved a singular victory on the domestic front — signing health care legislation — and attained the foreign policy achievement of reaching an arms control agreement with Russia that calls for the two nuclear powers to slash their nuclear arsenals to the lowest levels in half a century.

Mr. Obama’s visit to Afghanistan came amid tension between the two countries that has not substantially abated since Mr. Karzai’s was declared the winner of an election tainted by fraud. In the wake of the election, the Americans, the United Nations and other NATO countries demanded that Mr. Karzai make major overhauls in the electoral system, tacitly indicating that they might withhold money for the next election if they did not see changes.

Mr. Karzai recently overhauled the election complaint commission, but made it less neutral by arrogating to himself the right to appoint all five members. Currently three of the members are appointed by the United Nations. The move infuriated some Western diplomats here who saw it as almost a taunt.

Further compounding Mr. Karzai’s grievances was the conference in London at the end of January at which corruption was one of the major topics and Western officials again made clear that they felt Mr. Karzai had fallen short. Recently, he has strengthened the anti-corruption commission, and the attorney general appears to be moving forward on a handful of high-profile cases involving former government figures, but corruption remains pervasive and Mr. Karzai has not used his position as a bully pulpit to change the culture.

“He’s slipping away from the West,” said a senior European diplomat in Kabul.

Mr. Karzai received Iranian President Mahmoud Ahmadinejad on an official visit to Kabul in early March and met with him again this past weekend in Tehran when the two celebrated the Afghan and Iranian new year together. Mr. Karzai returned to Kabul only hours before Mr. Obama landed.

Last week, Mr. Karzai made a three-day trip to China, a country that is making economic investments in Afghanistan, notably its copper reserves, taking advantage of the hard won and expensive security efforts of the United States and other western nations.

Air Force One landed at nighttime at Bagram Air Base after a 13-hour nonstop flight for a visit shrouded in secrecy for security reasons, and Mr. Obama quickly boarded a helicopter for the trip to Kabul.

White House officials did not disclose advance notice of the trip, and even went as far as informing reporters that Mr. Obama would be spending the weekend at Camp David with his family. In fact, the president’s trip occurred during the Afghan night, and he was flying back to Washington before most Afghans awakened Monday morning.

Besides General Jones, Mr. Obama was accompanied by Rahm Emanuel, his chief of staff, and a number of other officials from the White House and the Defense Department.

Mr. Obama also met with some of the tens of thousands of American troops who have been sent to Afghanistan since he took office. His visit with the troops is particularly significant because it comes at the same time as military reports that the number of American troops killed in Afghanistan has roughly doubled in the first three months of 2010, compared to the same period last year.

The number of soldiers wounded in combat has also spiked dramatically. Military officials have warned that casualties are likely to continue to rise sharply as the Pentagon completes the deployment of 30,000 additional soldiers, under the strategy that Mr. Obama announced in November. The reason for the spike, military officials said, is because American forces are aggressively seeking out Taliban insurgents in the country’s population centers, and are planning a major operation in Kandahar, the spiritual home of the Taliban, in the coming months.

At Bagram Air Base, Mr. Obama told the cheering troops that he had no doubt they would be successful in their efforts to stop the Taliban from regaining power.

“Al Qaeda and their extremist allies are a threat to the people of Afghanistan and a threat to the people of America, but they’re also a threat to people around the world,” Mr. Obama said. “My main job here today is to say thank you on behalf of the entire American people. You are part of the finest military in the history of the world. And we are proud of you.”

The visit with American troops from their commander in chief was a long time coming. While Mr. Obama visited troops at Camp Victory in Iraq three months after he was inaugurated, the White House had held off on a presidential trip to Afghanistan as Mr. Obama went through a rigorous months-long review of Afghanistan strategy, and as that country endured the twists and turns of a disputed election.

Even after Mr. Karzai was inaugurated and Mr. Obama announced that he would send an additional 30,000 American troops, Mr. Obama still put off the visit as he focused on the machinations around his domestic priorities, including a health care bill.

Indeed, some members of the military have privately expressed concern that since announcing the Afghanistan troop increase, Mr. Obama has not talked much about the war there.

Mr. Obama appeared to be trying to address that on Sunday during his remarks with Mr. Karzai. “One of the main reasons I’m here is to just say thank you for the incredible efforts of our troops and our coalition partners,” he said. “They make tremendous sacrifices far away from home, and I want to make sure they know how proud their commander in chief is of them.”