Said Tayeb Jawad predicted the runoff would follow an announcement expected within days by the U.N.-backed electoral commission looking into fraud in the August election.
The ambassador is the first official from Karzai's government to predict publicly that the challenger, Abdullah Abdullah, will have enough support to force a runoff. Jawad said all sides should work hard to hold the runoff vote swiftly - ideally within a month.
A two-week deadline mandated in the country's constitution is "impossible," Jawad said. He worried that if the deadline slipped far into November, the weather will be too cold in parts of the country. Voters in Afghanistan, a country of great distances and few roads, often must travel long distances and spend significant time outdoors.
CBSNews.com Special Report: Afghanistan
Jawad spoke at the U.S. Institute of Peace, and afterward with The Associated Press.
"To delay until spring is a recipe for disaster," Jawad said, because Afghanistan needs clear leadership. Delay would also undermine the Afghan government's relationship with the United States, he said.
"We will have ... a government under pressure to deliver results" but with its top leadership in limbo, Jawad said.
The U.N.-backed Electoral Complaints Commission, which is tasked with determining how many fraudulent votes to toss out, could release its findings as early as Saturday. The nation's main electoral body would then announce whether Abdullah will face Karzai in a runoff, which would have to be held within two weeks.
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A Western diplomat with knowledge of international discussions surrounding the election said Thursday that if disqualification for fraud take Karzai below 50 percent, the United Nations will take the position that a second round is required unless the candidates agree to an alternative arrangement. The diplomat briefed reporters on condition of anonymity because of the sensitivity of the issue.
Uncertainty over the election has eaten away at Karzai's legitimacy as the Taliban-led insurgency in the countryside deepens and the Obama administration debates its strategy in a war that has become increasingly unpopular in the U.S.
CBS News Special Report: The Road Ahead
"While the international community is reviewing its policy, it's crucial that the process end with an outcome which leads to a legitimate government which could be a partner for the international community ... and deal with the challenges which are ahead of it," Abdullah told reporters on the lawn of his home in Kabul on Thursday.
Abdullah's camp believes a runoff is imminent. Karzai spokesman Waheed Omar said Thursday he expects otherwise.
"If that process remains technical, remains transparent and remains accountable, we do not see a chance for the elections to go to a second round," Omar said. He said he based his comment on reports from Karzai representatives who observed the opening and examining of ballot boxes.
Preliminary results show Karzai won re-election with about 54.6 percent of the vote, but the commission could discard enough fraudulent ballots to drop his tally below 50 percent and force a second round.
Both candidates rejected rumors that they might agree to some sort of power-sharing deal or coalition government rather than risk a runoff that will likely be plagued by more violence and could be hampered in the north by winter snow that cuts off mountain villages.
The top U.N. official in Afghanistan has acknowledged "widespread fraud" occurred in the Aug. 20 poll.
Also Thursday, the fourth-place finisher said President Barack Obama's security reputation could be riding on the war in Afghanistan.
Ashraf Ghani said U.S. attention has been focused primarily on whether to boost U.S. troop strength there and by how much. There is a "lack of clarity" about political issues and corruption problems, Ghani said.
"Obama's credentials in the security field depends on getting this right," Ghani said in a speech and news conference at the Atlantic Council, also in Washington.