KABUL, Afghanistan — Hundreds of Afghans protested Saturday against alleged fraud in last week’s presidential runoff, part of escalating tensions over what Western officials had hoped would be a smooth transfer of power, as violence across the country killed at least 13.

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.

Abdullah announced this week that he was severing ties with the Independent Election Commission and would refuse to recognize 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 a third term.

The IEC’s official timetable says initial results are due on July 2. Independent Election Commission chairman Ahmad Yousuf Nouristani said Saturday that the commission would address or investigate any concern Abdullah had.

A thousand Abdullah supporters gathered in Kabul to protest against the electoral commission, accusing it of fraud and chanting: “Our vote is our blood and we will stand up for it!”

Hundreds of anti-riot police surrounded the demonstration, which was peaceful.

“We gather today to protest against the election commission, which is not an independent commission at all. They are conducting fraud for a specific candidate,” said Mohammed Ghani Sharifi, a 23-year-old protester. “The people are so upset and they cannot tolerate such fraud because the people took risks to cast their votes.”

While the vote was relatively peaceful, the Taliban had warned people not to participate and carried out several attacks.

In a separate demonstration, hundreds of Abdullah supporters marched from the northern part of the capital toward the airport, where they were stopped by a police roadblock.