Al Jazeera's Hoda Abdel Hamid, reporting from Irbil, said observers at polling stations across the region maintained that voting took place smoothly for the most part.
But just before the polls closed, the region's main opposition group told Al Jazeera that their observers had witnessed instances of fraud in some areas.
A spokesman for the Change List, the main opposition party, said fraud was especially "significant" in the extended hour of voting.
"Tens of thousands of security forces voted today when they should have voted on the 'Special Day'", he said, referring to Thursday, when Kurdish members of Iraq's armed forces were to cast their ballots.
"Many others who could not find their names on the registration lists, voted. We accuse the Iraqi high electoral commission of being biased and of doing nothing.
"We ... will soon issue a statement calling for the cancellation of the election, mainly in Irbil."
Our correspondent said the ruling Kurdistan Democratic Party (KDP) had dismissed the allegations of fraud as "completely baseless".
"[The party said] that is proof that the Change List had actually prepared these accusations before even waiting for the polling stations to shut down," she said.
A representative of the ruling alliance told Al Jazeera that he was not surprised by the allegations.
"It is too early to make accusations. Accusations have to be proved," he said.
"Those troops who voted today, they couldn't vote on the 'Special Day', so it is their right to vote today."
About 2.5 million Kurds were eligible to vote in the dual elections, a full six months after the rest of the country held provincial elections.
Five candidates registered for the presidential race, while 24 political lists were competing for the 111 seats in the regional assembly.
Massoud Barzani, the incumbent regional president, appears likely to be re-elected.
Barzani's Kurdistan Democratic Party (KDP) and the Patriotic Union of Kurdistan (PUK), headed by Jalal Talabani, the Iraqi federal president, are expected to sweep the parliamentary poll.
The two factions have dominated the region's politics for decades and have been in power since 1991 when the region became semi-autonomous.
Critics of the Kurdish regional government point to widespread official corruption, abuses by security forces, media intimidation and an atmosphere they say stifles dissent.
Tensions with Baghdad
The election comes amid tensions between the semi-autonomous Kurdish region and the central government in Baghdad.
|Barzani, left, is expected to be re-elected
as regional president [AFP]
On a national level, in the run up to the elections, tensions have been high between Barzani's administration and the central government of Nuri al-Maliki, the Iraqi prime minister, over Kurdish claims to 16 disputed areas.
Those areas include oil-rich Kirkuk, and parts of three historically Kurdish-populated provinces - Diyala, Nineveh and Salaheddin.
Barzani has insisted he will not "compromise" on the Kurd's longstanding claims to Kirkuk and wants the issue to be settled by a referendum - called for under the Iraqi constitution - despite opposition from Kirkuk's Arab and Turkmen residents.
The country's natural resources have increasingly become a point of disagreement with the central government and have hamstrung exploitation of much of Iraq's massive proven reserves.
On June 1, the Kurdish administration began exporting oil for the first time, but Baghdad is contesting the region's right to sign contracts without central government approval.