Castillo, who has rattled the Andean country's political establishment, finished with a narrow 44,000-vote lead with all ballots counted, though the result has been delayed with Fujimori alleging fraud and seeking to get votes disqualified.
That bid has appeared to falter, however, as potential allies have distanced themselves from Fujimori, the daughter of divisive ex-President Alberto Fujimori, who is currently in prison for corruption and human rights abuses.
"Enough already," said a weekend editorial in the conservative newspaper El Comercio, part of one of the most powerful media conglomerates in the South American country that has generally backed Fujimori.
"Today it is clear that what began with the use of legitimate legal resources to question the suitability of some ballots... has started to become an attempt by different political sectors to delay the process as much as possible."
Castillo's Free Peru party and the electoral body have denied any claims of fraud and international election observers have said the vote was carried out cleanly. The U.S. State Department went further, calling it a "model of democracy."
On Monday, Fujimori went to the government palace and delivered a letter to the interim president, Francisco Sagasti, requesting an international audit of the vote. Her claims have won backing by some voters and some retired military personnel.
The electoral jury, which was forced to halt reviewing contested ballots last week after one of the judges tendered his resignation, resumed its work on Monday to complete the process, needed to announce the final result.
CENTRAL BANK CHIEF?
The tight election has split the country between wealthier urban elites and poorer rural areas. On Saturday thousands of Peruvians on both sides took to the streets amid uncertainty over the outcome. read more
Castillo, a 51-year-old former teacher and son of peasant farmers, has shaken up investors and mining firms with plans to rewrite the Constitution and keep a larger share of profits from mineral resources including copper.
He has, however, looked to temper those fears by appointing more moderate economic advisers and on the weekend he said he wanted to retain well-respected central bank head Julio Velarde, a key signal of stability to markets. read more
Pedro Francke, a left-leaning economist who is now economic spokesman for Castillo, said the candidate had spoken on Monday with Velarde, who had been due to step down in July at the end of the current administration.
"Institutionallly, this is the most important thing," Francke told Exitosa local radio, adding that there was still work to do to convince Velarde to stay.
"In fact Julio Velarde himself has said 'Well, I'm a little tired, I'll think about it.' And well, we have agreed to talk later when Pedro Castillo has been officially confirmed and so we can set up a formal meeting," Francke said. Reporting by Marco Aquino; Editing by Adam Jourdan and Dan Grebler