Right-wing presidential candidate Keiko Fujimori admitted she was headed for defeat, but pledged to mobilize her supporters and lashed out against Castillo as having won in an "illegitimate" manner.
Castillo came out of the June 6 run-off vote ahead by a scant 44,000 vote margin. The official result has been delayed by appeals from Fujimori aimed at annulling some ballots over fraud accusations, despite little evidence.
Fujimori said she was bound by law to recognize the official election result.
"I am going to recognize the results because it is what the law and the constitution that I have sworn to defend, mandates. The truth is going to come out anyway," she told reporters.
The National Jury of Elections said earlier on Monday it had tossed out the last appeals by Fujimori, a conservative who is the daughter of jailed former President Alberto Fujimori.
"They have stolen thousands of votes from us," Fujimori said at a news conference. She called on her followers to protest.
"We have the right to mobilize... but in a peaceful manner and within the framework of the law," she said.
The Organization of American States, European Union and Britain have all said the election was clean.
Castillo is set to take office on July 28 for a five-year term as leader of the world's second largest copper-producing nation.
A 51-year-old former school teacher and the son of peasant farmers, Castillo has pledged to redraft the constitution and hike taxes on mining firms, but has in recent weeks softened his rhetoric and hinted at a more moderate, market-friendly approach. Reporting by Marco Aquino; Writing by Hugh Bronstein and Adam Jourdan; Editing by Rosalba O'Brien