A near-complete count showed Kuczynski, 77, had 50.3 percent of the vote to 49.7 percent for Fujimori, the daughter of a jailed former president, but the result remained too close to call.
Both have vowed to heal divisions dating to the violent period of rule by Fujimori's father Alberto in the 1990s. He is in prison for corruption and for massacring alleged terrorists.
With nearly 93 percent of ballots counted, just over 100,000 voters separated the two candidates, the national elections office said.
"We are hoping to have a government of consensus. No more fighting and confrontation," he said late Sunday, waving from a balcony.
Fujimori, 41, also urged her supporters to sit tight.
"We are going to wait cautiously because the results will be coming in all night from the regions, from overseas, and the rural vote from deepest Peru. For that reason we are optimistic," she said.
"We have seen the vitality of Peruvian democracy and that fills me with pride."
They vowed to fight crime and create jobs in the nation of 31 million people, a major source of minerals and cocaine.
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