The U.S. special envoy to Afghanistan, Richard Holbrooke, recently held an "explosive" meeting with Afghan President Hamid Karzai over the country's presidential election, according to several news reports.

At a private lunch held on August 21, one day after the election, Holbrooke reportedly pressed Karzai on widespread state-engineered ballot-rigging alleged by his primary opponent, former foreign minister Abdullah Abdullah.

Holbrooke is said to have twice proposed holding a second run-off election after he expressed concern over voter fraud allegations. Karzai reacted "very angrily" to the suggestion and the meeting ended shortly after.

According to the BBC, the meeting was described as "explosive" and "a dramatic bust-up."

"It was a difficult meeting and there were some sharp exchanges in it," an unnamed U.S. official with knowledge of the meeting told AFP.

Karzai enjoyed a warm relationship with former President George W. Bush, but relations are believed to have since cooled under President Barack Obama.

Afghan election officials have released two batches of vote tallies that show President Karzai with 44.8 percent of the vote and top challenger Abdullah with 35.1 percent, based on returns from 17 percent of polling stations. The next partial results are expected Saturday.