The demand was made on Tuesday by Jesus Ortega, the campaign manager for the candidate from the Democratic Revolution Party, Andres Manuel Lopez Obrador.
Supporters of Lopez Obrador say that preliminary results giving victory to Felipe Calderon, his conservative rival, by about 400,000 votes were manipulated.
The official count by the autonomous Federal Electoral Institute starts on Wednesday and could take days. Even if a winner is declared, those results can be challenged in court.
Calderon's apparent win caused financial markets and the peso to rally for a second day on Tuesday.
The former energy secretary, representing the National Action Party of Vicente Fox, the president, told Radio Formula that "the people are right, the markets are right" in assuming that he has won.
Mexico must focus on the future, he said in an interview with the station. "The problems are big, but Mexico is bigger than its problems," he said.
There were some fears that Lopez Obrador's refusal to accept Calderon's apparent victory could send the country into turmoil. Allegations of irregularities threaten to drag out the process for weeks.
"We are going to employ whatever legal means"
Andres Manuel Lopez Obrador, presidential candidate
Tensions were high on Tuesday in the southern state of Oaxaca, where striking teachers occupied businesses, boarded buses and blocked roads despite pledges to halt their sometimes violent campaign until the presidency had been decided.
Speaking to reporters at his campaign headquarters on Monday night, Lopez Obrador said: "There are about three million votes missing."
The former mayor of Mexico City said officials had estimated a voter turnout of 41 million or 42 million, yet preliminary vote tallies by the electoral institute showed only about 38 million ballots cast.
As a result, the institute's first count is something that "we cannot accept", he said.
Both candidates had declared victory on Sunday night, but representatives of Roberto Madrazo, of the Institutional Revolutionary Party, or PRI, conceded defeat on Monday night.
Calderon claimed victory on
Lopez Obrador continued to claim victory, saying: "We have a commitment to the citizens to defend the will of millions of Mexicans.
"We are going to employ whatever legal means."
He said there were "many irregularities" in the election, including badly reported results and the double-counting of votes. He also asked how it was possible that his party won 155 of 300 electoral districts without winning the presidency.
In an interview on Tuesday with the Televisa network, Luis Carlos Ugalde, the electoral institue's president, said officials would review any problems during the official count.
After 98.45% of the polling stations had reported, Calderon had 36.38% and Lopez Obrador had 35.34%. Madrazo had 21.57%.