The Kurds had originally voted in favour of the law last week when it was passed in parliament, but they say it was only over the weekend that they found out their provinces had received fewer seats than they believe they deserved.
Parliament was expanded from 275 to 323 seats to reflect population growth, but only three of the new seats were allocated to Kurdish provinces, giving them 38 total, according to the Independent High Electoral Commission's website.
Other regions saw much larger growth. For example, Ninevah province which borders the Kurdish region, grew from 19 seats to 31. Basra province in the south grew from 16 seats to 24.
Mahmoud Othman, a Kurdish member of Iraq's national parliament, echoed Barzani's demands and said the Kurds had been expecting about 17 additional seats.
"The main point is the allocation of seats," Othman told The Associated Press. "If no changes are made on this matter then we will not participate in the elections."
"If no changes are made on this matter then we will not participate in the elections"
Mahmoud Othman, Kurdish member of Iraq's national parliament
Three northern provinces make up the Kurdish autonomous region, and are represented by their own parliament as well as president.
While Kurds have experienced bitter political struggles between themselves in their autonomous region, they have generally presented a strongly united front on the national political scene.
The Kurdish demands follow those of Tariq al-Hashemi, the Arab vice president, who threatened on Sunday to veto the election bill unless voters outside Iraq were guaranteed more seats.
The US has tied its withdrawal of all combat troops to the national vote and US military officials have said they will begin to draw down forces about 60 days after the election, hoping for assurances by then that Iraq is on stable footing.
Under a plan by Barack Obama, the US president, all US combat personnel must be out of Iraq by the end of August 2010. The rest of the troops, such as trainers and support personnel, must leave by the end of 2011.