"We need Iraqi security to be sent to Kirkuk immediately to protect the lives of Electoral Commission staff members who are now surrounded by protesters", Taha said in the announcement.
Riyadh al-Badran said the gunmen, whom he did not identify, were pressuring the commission to change the election results in the multi-ethnic region.
The head of Iraq's national election commission said at a news conference that armed men had taken over the election office and that the workers inside were "in effect, hostages", but local officials and witnesses disputed that account, saying there was no sign of weapons at what appeared to be a peaceful demonstration. Oil-rich Kirkuk is at the heart of a long-running dispute between the Kurds, who claim it as part of their autonomous region, and the central government in Baghdad. Such hostages situations might become a growing problem if the recounts are expanded nationwide, as Prime Minister Hayder al-Abadi has suggested.
"Everyone is asking for one thing only, we are asking for the ballot boxes to be open, even if it's just one box", said Sheikh Amer al-Jabouri, one of the demonstrators.
Badran said that figure should be announced in the next two days.
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Saturday's elections were the first since the defeat of IS a year ago by Iraqi forces backed by a US-led coalition, but the turnout fell far short of previous elections with only 44.5 percent of registered voters participating.
Roughly half of Kirkuk's population is Kurdish, with around a quarter Arab and a fifth Turkmen.
Iran-backed Shia militia chief Hadi al-Amiri's Fatah (Conquest) coalition was in second place, while Abadi's Nasr (Victory) coalition is in third.
Reports indicate that Sairoun Alliance - a coalition of Shia cleric Muqtada al-Sadr and the Iraqi Communist Party - won the national popular vote with more than 1.3 million votes, gaining 54 seats in parliament out of a total of 329.
Saturday's election was the first since the defeat of Islamic State of Iraq and the Levant (ISIL). The turnout was 15 percent lower than in 2014.