The move quashed hopes for a political dynasty for Kirchner and his wife, President Cristina Fernandez de Kirchner, The New York Times reported. The resignation appeared to put Argentina's presidency up for grabs in the 2011 elections, the newspaper said.
As president, Nestor Kirchner had led the country out of its economic crisis in 2001. In this election, he had run for the lower house of Congress in hopes of helping the administration of his wife.
Nestor Kirchner ran in Buenos Aires province, the country's most populated, where he lost to a millionaire congressman, Francisco de Narvaez.
Kirchner's supporters also suffered heavy losses, and he and his wife lost control of both houses.
Critics have blamed the Kirchners for the flight of capital from the country and a decline in foreign investment, the Times said.