The count was under way on Sunday in Iraqi Kurdistan's first election in four years, with opposition groups hoping to end the decades-old dominance of the two main ex-rebel parties.
The vote itself went off largely without incident on Saturday, with turnout pegged at 73.9 percent.
But sporadic violence hit the main opposition grouping in the run-up to the election, and one man was reported killed in a shooting after polls closed.
The United Nations praised the "smooth conduct" of the vote, while the British embassy in Baghdad termed it "a significant step" and said the turnout was "very impressive."
Preliminary results are due in the coming days.
The election for the autonomous region's parliament came as two and a half years of turmoil around the Middle East raised renewed questions about the political future of the Kurds, who are spread across a number of neighbouring states.
Supporters of Iraqi Kurdistan's biggest bloc, the Kurdistan Democratic Party of regional president Massud Barzani, took to the streets of regional capital Arbil after polls closed, honking car horns, waving KDP flags and firing off celebratory gunfire.
Similar scenes were reported elsewhere in the three-province autonomous region, with supporters of various parties in a festive mood.
About 2.8 million Kurds were eligible to vote.
The campaign centred on calls for more to be done to fight corruption and improve the delivery of basic services, as well as on how the energy-rich region's oil revenues should be spent.
The elections, the first since July 2009, saw three main parties jostling for position in the 111-seat Kurdish parliament, with implications beyond Iraq.
The KDP is widely expected to win the largest number of seats, although it is unlikely to obtain a majority on its own.
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But the Patriotic Union of Kurdistan (PUK), which for decades has held a duopoly on power alongside the KDP, faces a challenge from the Goran movement in its Sulaimaniyah province stronghold.
The challenge has been heightened by leadership questions as the party's veteran chief, Iraqi President Jalal Talabani, recuperates in Germany from a stroke.
After polls closed in Arbil, one man -- apparently a PUK supporter -- was reported killed in a shooting, although election officials insisted the death was unconnected to the vote.
Internationally, the focus is likely to be on the region's drive for greater economic independence from the federal government, with which it is locked in multiple disputes over oil revenues and territory.
Arbil has sought to establish a pipeline that would give it access to international energy markets, sent crude across the border to neighbouring Turkey, and signed deals with foreign energy firms.
It has also capitalised on its reputation for greater safety and stability, as well as a faster-growing economy than the rest of Iraq, to solicit investment independent of the federal government.
All this has angered Baghdad, and the two sides are also locked in a protracted dispute over the Kurds' long-standing demands for the incorporation of other traditionally Kurdish-majority areas into their autonomous region.
The region has also become increasingly embroiled in the conflict in Syria.
Clashes last month between Kurdish forces and jihadists seeking to secure a land corridor connecting them to Iraq pushed tens of thousands of Syrian Kurds across the border, seeking refuge in Iraq's Kurdish region.
Barzani has threatened to intervene in the Syrian conflict to protect Kurdish civilians, although officials have since rode back on those remarks.
Iraqi Kurdistan enjoys a high level of autonomy from Baghdad, and the regional parliament has passed laws on a wide range of issues.
Kurdistan also operates its own security forces and visa regime and has control over an array of other responsibilities.