By Ian Pannell
BBC News, Kabul
Mr Karzai was elected president of Afghanistan in 2004
The US special envoy to Afghanistan has held an "explosive" meeting with Afghan President Hamid Karzai over the country's election, the BBC has learnt.
Richard Holbrooke raised concerns about ballot-stuffing and fraud, by a number of candidates' teams, sources say.
The US envoy also said a second-round run-off could make the election process more credible, the sources said.
Concerns have already been raised about Afghanistan's election, although final results are not due until September.
A number of senior sources have confirmed the details of a meeting between Mr Holbrooke and Mr Karzai held on 21 August, one day after the election.
The meeting was described as "explosive" and "a dramatic bust-up".
Mr Holbrooke is said to have twice raised the idea of holding a second round run-off because of concerns about the voting process.
He is believed to have complained about the use of fraud and ballot stuffing by some members of the president's campaign team, as well as other candidates.
Mr Karzai reacted very angrily and the meeting ended shortly afterwards, the sources said.
However, a spokeswoman for the US embassy in Kabul denied there had been any shouting or that Mr Holbrooke had stormed out.
She refused to discuss the details of the meeting.
A spokesman for the presidential palace denied the account of the conversation.
There have been many doubts raised about the Afghan presidential election, about the turnout and irregularities.
But this is the first time that a leading Western official has apparently expressed it quite so openly.
It will raise more questions about the credibility of the whole process and could well make the plan to establish a meaningful government in a stable country all the harder to achieve.