Official results for the election, held the same day as Iraq's historic national vote on January 30, have not yet been released.
But Turkmen and Arab parties in the city, a longstanding ethnic tinderbox, say Kurds from other parts of the country flooded Kirkuk on election day to inflate the community's vote.The Kurdish list expects to get about 63 percent of the vote for the Tamim provincial council, which includes Kirkuk, according to the Kurdish media.
"The elections lack credibility because of the major violations and the absence of international observers," a Turkmen candidate for the provincial council, Saadeddin Arkaj, told AFP after a meeting of Turkmen parties.
Arkaj said the Iraqi election commission should review the vote count and investigate the complaints. "The results fixed by the Kurds will cause a catastrophe," he warned.
"The Turkmen cannot accept this plot through which the Kurds want to join Kirkuk to Kurdistan," added Arkaj.
An Arab candidate for the provincial council, Abdel Rahman Munshid al-Assi also called the election a "plot". Thousands of Kurds were brought from the provinces of Suleimaniyah and Arbil on January 30 "to vote a second time in Kirkuk," he said.
"They are aiming to attach Kirkuk to Kurdistan and we Arabs and Turkmen reject this," he said after a meeting of Arab and Turkmen parties late Saturday.
"We are examining all options as we will not have a real presence on the provincial council. Two thirds of the seats will go to Kurds," Assi predicted.
Kurdish leaders deny any vote fraud.
"Unfortunately, the Arabs and Turkmen do not understand democracy," said Rajkar Ali, a candidate for the Patriotic Union of Kurdistan for the election.
"We are not seeking to wipe out the presence of our Arab and Turkmen friends, we want to win back the rights that were taken from the Kurds," he said.
A decision brokered in January by the interim Iraqi government gave tens of thousands of displaced Kurds the right to vote in Kirkuk, effectively tipping the balance to the Kurdish community and drawing the ire of neighbouring Turkey.
Sunni and Shiite Arab parties withdrew from the local election in Tamim province in protest.
Former Iraqi president Saddam Hussein sought to Arabise Kirkuk by moving Kurds away and bringing in Arabs from other parts of the country. Leaders of the Kurdish autonomous region want Kirkuk to be part of their region.
Kirkuk is important to Iraq because of its oil wealth but leaders of the autonomous Kurdish north have openly said they want control of the city.
Turkey, which has its own Kurd rebellion, worries about Kurds using Kirkuk as a capital of an independent state. It has accused the United States of not doing enough to contain Kurdish groups in Iraq.
US Secretary of State Condoleezza Rice, in Turkey on Sunday, sought to reassure Ankara that Washington wanted a united Iraq and that it would not allow attacks in Turkey from Kurdish rebel bases in Iraq.