Former foreign minister Abdullah Abdullah, who is running against Ashraf Ghani Ahmadzai, a former finance minister, has accused electoral officials and others of trying to rig the June 14 vote against him.
Mr Abdullah announced he was severing ties with the Independent Election Commission (IEC) and would refuse to recognise any results it releases.
He also suggested that the United Nations step in, an idea supported by President Hamid Karzai, who is constitutionally barred from seeking a third term in office.
The IEC's official timetable says initial results are due on July 2. The body's chairman, Ahmad Yousuf Nouristani, said yesterday that the commission would address or investigate any concerns that Mr Abdullah had.
About one thousand Abdullah supporters gathered in the capital, Kabul, to protest against the electoral commission, chanting: "Our vote is our blood and we will stand up for it!"
Hundreds of anti-riot police surrounded the demonstration, which went ahead peacefully. Violence in the country in the run-up to the elections had resulted in the deaths of 13 people.