"We want unity in this election, not a boycott," ethnic Tajik commander Yunus Qanuni told reporters in Kabul on Monday after intermediaries, including US envoy Zalmay Khalilzad, interceded in the row.
"The people want it and we appreciate their feelings," he said.
Qanuni said he was speaking for several candidates but not all. But his acquiescence means the end of the most serious opposition to the poll, which was held under the shadow of threats of violence by the ousted Taliban.
The election commission, the Joint Election Management Body, earlier on Monday announced a panel would investigate irregularities and asked Karzai's rivals to submit any complaints by Tuesday evening.
Officials face difficulties in taking
ballot boxes to counting centres
A commission official said counting, which could last for three weeks, would start on Wednesday.
Delays were expected because of difficulties in taking ballot boxes to counting centres. In the rugged Hindu Kush mountains, the ballots will be brought down by donkey.
One candidate said Qanuni and Hazara chieftain Muhammad Muhaqiq had been persuaded to drop out of the opposition boycott.
"Khalilzad urged them to do so in return for accommodating them somehow in the future government," the candidate said.
General Abd al-Rashid Dustum, an ethnic Uzbek candidate and strongman in the north, was due in Kabul within hours for consultations with the US envoy.
Millions of Afghans took part in polls on 9 October, the first time the nation voted for a president, but all 15 of Karzai's challengers announced a boycott, saying a system to prevent multiple voting had failed.
The dispute over the poll resulted from ink daubed on voters' fingers to prevent them from voting repeatedly.
"We want unity in this election, not a boycott"
Some election workers used the wrong pen to mark voters, and the ordinary marker ink was quickly washed off.
Fears of multiple voting had been stoked by the late issue of a high number of voter cards - 10.5 million in a population of about 28 million, only about half of which are adults.
Karzai and 17 other candidates were on the ballot but two withdrew in favour of the president. The winner needs 51% of the vote, otherwise a run-off between the top two candidates will be held in November.