Afghanistan's Independent Election Commission (IEC) cancelled a runoff vote for the presidency on Monday after Abdullah Abdullah, a former foreign minister and Karzai's only rival in the presidential runoff scheduled for November 7, withdrew from the race.
The commission then declared Karzai, in power since the Taliban were toppled by the US invasion in 2001, the winner.
"The democratic process would have been better if our colleague Abdullah Abdullah had participated in this process and the second round had taken place," Karzai told reporters.
"... it did not happen, but again we are happy the constitution was respected ... it went in the right way."
Al Jazeera's James Bays, reporting from Kabul, the Afghan capital, said that Karzai had set "a very conciliatory tone" in his speech.
"Special mention of Abdullah Abdullah, who he mentioned had got about half a million votes, actually it was closer to one million," he said.
"Is he going to offer an olive branch to Dr Abdullah and his supporters and offer them some seats in his cabinet? That is certainly what he has ben urged to do by members of the international community.
"But Hamid Karzai has made many promises to those who supported him in that first round on August 20. Sources tell Al Jazeera that he has promised a lot of positions already to many people who backed him."
Said Azam, an Afghan political analyst, told Al Jazeera that he thought it was unlikely Karzai would offer a post to Abdullah himself.
"I think that the role that Karzai is expecting from Dr Abdullah is that of opposition leader rather than being part of his government," he said.
"I think he does not assume that Dr Abdullah would accept a post in his cabinet and he is also not ready to offer him a role."
Abdullah has previously ruled out joining Karzai in any national unity government, but there are believed to have been negotiations between representatives of the two sides over a possible role for the challenger's supporters in the new administration.
Meanwhile, the Taliban said that the outcome of the election, which has been marred by violence and widespread fraud, showed that the real decisions about Afghanistan were made by the United States and its allies.
Karzai's second term in office adds pressure on the US in considering Afghan strategy
"The cancellation of the second round of elections has shown that the decisions about Afghanistan are made in Washington and London, even though the announcement took place in Kabul," the group said in a statement.
"What is surprising is that just two weeks ago in the election they said the votes belonging to puppet Karzai were all fraudulent, and not acceptable.
"But now with these fake votes, they have selected Karzai, and immediately Washington and London have sent Karzai messages of congratulations."
Barack Obama, the US president, was among the world leaders who congratulated Karzai on his re-election but also called on him to tackle corruption.
"I emphasised that this has to be a point in time in which we write a new chapter based on improved governance, a much more serious effort to eradicate corruption [and] joint efforts to accelerate the training of Afghan security forces," Obama said after phoning Karzai.
'Stain' of corruption
During Tuesday's news conference, Karzai said: "Afghanistan has been defamed by corruption. Our government has been defamed by corruption.
"We will strive, by any means possible, to eradicate this stain."
Washington is currently considering its options in Afghanistan, with General Stanely McChrystal, the US and Nato commander in the country, believed to be calling for up to 40,000 additional troops to be deployed.
The discovery of widespread fraud in the first round on August 20 resulted in Karzai's share of the vote falling below the 50 per cent threshold needed to avoid a runoff.
Ballot-box stuffing and distorted tallies led to more than one million votes in favour of the incumbent being thrown out.
The validity of the electoral process and the independence of the IEC have both been called into question.
Abdullah cited the government's refusal to accept his demands for changes to the IEC for his decision to boycott the runoff.