The conservative presidential candidate is poised to win the tightly fought leadership contest after she consolidated an unassailable lead over her leftist rival Roberto Sanchez late on Tuesday.
With 99.87 percent of ballots counted, Fujimori had secured more than 44,000 votes over Sanchez, according to the electoral authority.
Only around 36,300 votes remain to be tallied from 121 polling station records, making it impossible for the left-wing candidate to get ahead.
Fujimori thanked Peruvians for supporting her at a press conference.
Although the count was ongoing, the figures showed “a result that would be irreversible,” she said.
The polarising presidential race and the narrow margin that separated her from her rival had “fragmented” Peru, she conceded.
Fujimori’s victory would mark the return of her family name to power, more than two decades after the fall of her father, former president Alberto Fujimori.
He led Peru through the turbulent 1990s, crushing Maoist Shining Path rebels and taming hyperinflation.
But Fujimori senior was later disgraced, exiled and jailed for corruption and crimes against humanity.
Sanchez said he would not recognise a government headed by Fujimori, claiming a “serious violation of the electoral process.”
He alleges administrative irregularities in the handling of the overseas vote, which represents around 300,000 ballots, by the electoral authority.
The election has been one of the tightest Latin American leadership contests in decades, with crime and political instability dominating a race to choose the country’s ninth leader in a decade.
The winner will replace interim president Jose Maria Balcazar on July 28 for a five-year term. (AFP)
