The Afghan president's relations with the West have cooled since he was first elected in 2004, amid allegations of widespread corruption in his administration.
On Monday, US President Barack Obama asked 51-year-old Mr Karzai to intensify efforts to eradicate it.
Mr Obama - currently considering whether to send up to 40,000 more troops to Afghanistan - said Mr Karzai would be judged on deeds, not words.
"Our government has been seriously discredited by administrative corruption," said Mr Karzai on Tuesday.
Ian Pannell, BBC News, Kabul
Hamid Karzai has been left in no doubt by his international sponsors of what they expect from him.
And in his news conference he appeared to deliver. He said he would eradicate the stain of corruption that has dogged his government. He said he would build an administration for all Afghans and attempt to heal the growing ethnic divisions in the country.
And he appealed to what he called his Taliban brothers to agree to talks to bring peace to the country.
But the West has made it clear that he'll be judged on his actions, not his words, and crucial decisions about the level of foreign engagement and troop levels in the country will now depend upon it.
"We will try to remove this stigma from our soil and our country in any possible way."
He said he would work with anyone, whether they had opposed or supported him in the election.
And he continued: "We call on our Taliban brothers to come home and embrace their land."
But a now-resurgent Taliban - who were driven out of Kabul in late 2001 by US-led coalition forces, paving the way for Mr Karzai to take power - rejected his overture.
"What is astonishing is two weeks ago they were arguing that the puppet president Hamid Karzai was involved in electoral fraud... but now he is elected as president based on those same fraudulent votes, Washington and London immediately send their congratulations," said a Taliban statement.
The militants, who carried out attacks across the country during the first round, had vowed to disrupt the run-off, too.
In the initial ballot, hundreds of thousands of votes were discounted, including almost a third of those cast for Mr Karzai.
US President Barack Obama: ''The process was messy''
His share of the vote was cut to just under the 50% threshold needed for outright victory, requiring a second round to be held.
Dr Abdullah was adjudged to have won a third of valid ballots in August's vote.
One of the reasons for holding a deciding vote had been to try to restore some legitimacy to the process.
But Afghan election officials said on Monday the second round - which Mr Karzai had been the favourite to win - was being scrapped to save money and for security reasons.
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