If Kirchner wins, she would be the first woman to lead Argentina.
Early results showed Kirchner, candidate of the Peronist Party, leading former Finance Minister Roberto Lavagna and Congresswoman Elisa Carrio, The New York Times reported. Other candidates accused Kirchner of election fraud.
"Each time a citizen went to vote, the voting authority at the table said there aren’t ballots for your party," said Patricia Bullrich, Carrio's campaign manager. "'They said: ‘OK, you still have to vote. Vote for a blank slate, but you have to vote.'"
If Kirchner fails to win 45 percent of the vote, there will be a runoff. Pre-election polls put her right on the edge.
Nestor Kirchner guided Argentina through a major economic crisis after becoming president. Political observers believe he will run for president again in four years, the newspaper said.