Iraq's election commission says some of the complaints are "serious"
Claims of election fraud in Iraq are being investigated, as the counting from the weekend's election continues.
Sunni Arab tribal leaders in western Anbar province say they have hundreds of documents proving irregularities.
Iraq's deputy prime minister, who is himself a Sunni Arab, has called for a recount in Anbar.
Meanwhile, security measures to guard against unrest in the area are being put in place, a senior Iraqi army officer told AFP news agency.
Saturday's ballot in 14 of the 18 provinces was the most peaceful in Iraq since the fall of Saddam Hussein in 2003 and was seen as a test of stability before a general election, due later this year.
Allegations of election rigging are being made in many provinces, but the complaints in Anbar took a more serious turn when some of the heavily-armed tribes threatened violence. Tribal leaders have since agreed to ban the use of weapons.
Most Sunni parties did not participate in the last provincial elections in 2005 and Anbar has seen tension this time between Sunni Arab tribes and established parties that ran the province for years.
"Some of these complaints [about electoral fraud] are serious and could be considered 'red' complaints," Faraj al-Haidari, Iraq's senior electoral official, told Reuters. "Red" is the term for complaints which could alter the outcome of the vote.
2003: US appoints Governing Council
2004: Governing Council elects interim government
Aug 2004: National conference elects interim national assembly
Jan 2005: First general elections for transitional national assembly and provincial councils - Sunnis boycott vote
Dec 2005: General elections for first full-term government and parliament
Jan 2009: Elections for provincial councils - key test of security gains
Late 2009: General elections due
After meeting with tribal leaders in Anbar on Wednesday, Iraq's deputy prime minister Rafaa al-Issawi said: "We demand a recount of the votes and to bring to justice the people who committed fraud."
Turnout from the election was 51%, according to figures from the electoral commission, although this was lower than some predictions.
US President Barack Obama described the vote as "an important step forward".
Final results are not expected to be known for weeks.