Fujimori, a former congresswoman and the daughter of late ex-president Alberto Fujimori, remains in first place with 16.8 per cent of the vote in Sunday's election, according to the official tally, with about 80 per cent of ballots counted.
She is set to advance to a runoff expected to occur on June 7, with no candidate anywhere near the 50 per cent needed to win outright.
It is Fujimori's fourth bid for the presidency. A tight race is unfolding behind her, with right-wing former Lima mayor Rafael Lopez Aliaga in second place with about 12 per cent of the vote.
Centre-left candidate Jorge Nieto is close behind with roughly 11 per cent, according to figures from ONPE, the Andean nation's electoral authority.
Roberto Sanchez, a left-wing congressman, was in fourth place, with just over 10 per cent of the vote.
As counting continued, allegations of fraud started to spread more widely.
Lopez Aliaga, who earlier alleged a "brutal fraud" was taking place, was joined on Tuesday by Sanchez, who said he had concerns about the integrity of the process, though neither provided evidence to back their assertions.
European Union election observers said they had found no concrete evidence to support allegations of fraud that have circulated since Sunday, while acknowledging significant challenges.
"It is clear that there have been serious problems," Annalisa Corrado, head of the EU election observation mission to Peru, said in a press conference on Tuesday, local time.
She added that observers had "not found objective elements to support the narrative of fraud".
The prolonged vote count followed logistical failures that hampered the delivery of electoral materials on Sunday.
Authorities extended voting hours into Monday for more than 50,000 people who were unable to cast ballots on election day, mostly in parts of Lima, the country's capital and home to roughly a third of the electorate.
Piero Corvetto, head of Peru's electoral authority, appeared before Congress at lawmakers' request to explain the delays.
He denied that any serious irregularities had occurred, attributing the delays to an isolated error in the distribution of voting materials, and apologised for the disruptions.
The election, which included races for Congress, has posed numerous challenges for voters as well as electoral authorities, Corvetto added, following lengthy political turmoil in Peru that has eroded confidence in institutions and left many voters deeply disillusioned.
