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KABUL, Afghanistan — President Hamid Karzai, in his first speech since he was declared the winner of the much disputed presidential election, said Tuesday that he wanted to tackle corruption but made no specific commitments to reorganize his administration.

Moises Saman for The New York Times President Hamid Karzai of Afghanistan in Kabul on Tuesday made his first speech since being declared winner of the election.

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President Hamid Karzai of Afghanistan — pictured with with Marshal Muhammad Qasim Fahim, left, and Karim Khalili on Tuesday — made his first speech as a re-elected president in Kabul.

President Obama spoke to reporters on Monday after his telephone conversation with President Hamid Karzai of Afghanistan.

“Afghanistan has been tarnished by administrative corruption, and I will launch a campaign to clean the government of corruption,” he said.

Asked if that might involve changing important ministers and officials, he said: “These problems cannot be solved by changing high-ranking officials. We’ll review the laws and see what problems are in the law, and we will draft some new laws.”

He added that he would try to strengthen an anticorruption commission that was set up last year.

Although he said repeatedly that his government would seek to unify the country and that he wanted to work with all Afghans, he did not offer his former rival, Abdullah Abdullah, a place in the government and pointedly avoided answering questions about what role he might have.

His comments at a morning news conference followed an admonition from President Obama on Monday that he must take on what American officials have said he avoided during his first term: rampant corruption and the drug trade, which have fueled the resurgence of the Taliban.

After Mr. Karzai was officially declared the winner, Mr. Obama placed a congratulatory call in which he asked for a “new chapter” in the legitimacy of the Afghan government.

What he is seeking, Mr. Obama told reporters afterward, is “a sense on the part of President Karzai that, after some difficult years in which there has been some drift, that in fact he’s going to move boldly and forcefully forward and take advantage of the international community’s interest in his country to initiate reforms internally. That has to be one of our highest priorities.”

The administration wants Mr. Karzai and the Afghan government to put into place an anticorruption commission to establish strict accountability for government officials at the national and provincial levels, senior administration officials said Monday.

In addition, some American officials and their European counterparts would like at least a few arrests of what one administration official called “the more blatantly corrupt” people in the Afghan government.

Administration officials declined to provide the names of people they wanted to see arrested and acknowledged that such arrests were a long shot. The international community’s wish list of potential defendants includes Mr. Karzai’s brother, Ahmed Wali Karzai, a suspected player in the country’s booming illegal opium trade; Gen. Abdul Rashid Dostum, who is accused of involvement in the killings of thousands of Taliban prisoners of war early in the Afghan conflict; and one of Mr. Karzai’s running mates, Marshal Muhammad Qasim Fahim, a former defense minister who is also suspected of drug trafficking.

“A couple of high-profile heads on a platter would be nice,” said one European diplomat involved in Afghanistan. The diplomat, like other officials, spoke on the condition of anonymity because of the delicacy of the matter.

Obama administration officials have been pressing Mr. Karzai to take action against General Dostum and Mr. Fahim for several months. This summer, Mr. Obama even called for an investigation of General Dostum. Mr. Karzai instead allowed the general to return from exile and reinstated him to his government position, while the general endorsed Mr. Karzai and campaigned for him.

The corruption problem has surfaced repeatedly as Mr. Obama has been holding meetings to review his Afghanistan strategy, administration officials said.

“The issue of the government’s competence and legitimacy, and how that fits into our ability to succeed in Afghanistan, has been thoroughly discussed in these meetings,” a senior administration official said. “Because we’re putting American and coalition troops on the line in part to make sure the government stands and has a chance to succeed, there has to be an effort on their part to improve their effectiveness and address corruption.”

Administration officials said that the biggest leverage they had with Mr. Karzai was the number of American troops in Afghanistan, a number that could change as Mr. Obama saw fit.

White House officials said Monday that the resolution of the election would not affect the timing of their review of military strategy.

The White House press secretary, Robert Gibbs, said that the president’s announcement was still weeks away. Mr. Obama is expected to hold at least one more meeting with the Joint Chiefs of Staff and another with his national security advisers.

On Monday Mr. Obama appeared to acknowledge the tough road ahead. Mr. Karzai, Mr. Obama said, “assured me that he understood the importance of this moment.”

“But as I indicated to him,” the president said, “the proof is not going to be in words; it’s going to be in deeds. And we are looking forward to consulting closely with his government in the weeks and months to come, to assure that the Afghan people are actually seeing progress on the ground.”

Mr. Abdullah withdrew Sunday from a runoff that had been scheduled for Saturday to resolve the uproar over a fraud-plagued first round of voting in August. On Monday, Afghanistan’s Independent Election Commission announced there was no need for a runoff now that Mr. Karzai’s only competitor had withdrawn.

In Afghanistan, there had been little popular support for a unity government in which Mr. Abdullah would have a major role. For many Afghans a coalition government brings to mind the chaotic 1990s, when armed strongmen competed for turf in bloody battles that killed many Afghan civilians and destroyed large sections of Kabul.

Afghan political analysts as well as some citizens interviewed in Kabul said the election had undermined Afghans’ faith in democracy and strengthened the leverage of international players.

“This massive fraud has detracted from his authority and prestige,” Hamidullah Tarzi, an Afghan political analyst who served as a minister in two previous governments, said of Mr. Karzai. “Now the policy is not in the hands of Afghanistan. It is in the hands of the West.”

The pace of Mr. Obama’s review of Afghanistan policy drew sharp criticism on Monday from several Republican leaders in Congress. Additional delays, they said, could endanger troops and erode efforts to battle Al Qaeda and the Taliban in Afghanistan.

“Now that it is clear that President Karzai will remain in office, the White House has no further pretext for delaying the decision on giving General McChrystal the resources he needs to achieve our goals in Afghanistan,” said Representative John A. Boehner of Ohio, the House Republican leader, referring to Gen. Stanley A. McChrystal, the American military commander in Afghanistan. “There are no more excuses.”

Frederick W. Kagan, a military expert at the American Enterprise Institute who has advised General McChrystal, said that a decision in mid- or late November to add to American forces meant that most of those troops would not be in Afghanistan until April or May, past the beginning of what is traditionally considered the spring fighting season in the country.