The demonstrators, who are not necessarily linked to any particular party, say the vote was not fair.
They accuse Enrique Pena Nieto’s party, the PRI, of buying votes; some carried banners saying “Not another fraud”.
Enrique Pena Nieto, who was declared the winner after a recount of nearly half the votes, denies the allegation.
The second-placed candidate in Mexico’s presidential election, Andres Manuel Lopez Obrador, has said he will mount a legal challenge to the result.
Andres Manuel Lopez Obrador said he would prove that illicit money was used to buy votes in the 1 July poll and secure the victory of centrist candidate Enrique Pena Nieto, who denies this.
Six years ago, after losing the presidential election by a narrow margin, the left-wing Andres Manuel Lopez Obrador led weeks of protests that caused disruption in central areas of Mexico City.
Enrique Pena Nieto was confirmed the winner on Friday after a final recount, with 38.21% to Andres Manuel Lopez Obrador’s 31.59%.
Third-placed Josefina Vazquez Mota, from the right-wing National Action Party, has admitted defeat.
There is a broad spread of people, not necessarily from the left, who feel that votes in their parts of Mexico were tampered with.
But Andres Manuel Lopez Obrador, of the Party of the Democratic Revolution, said the election had been fraudulent and that he would file an appeal next week.
He accuses the party of Enrique Pena Nieto, the Institutional Revolutionary Party, of paying for votes using gift cards for a supermarket chain.
Numerous videos have emerged of people claiming they received credit in exchange for voting for the PRI.
The party governed Mexico for 71 years until it was defeated in the 2000 presidential poll.
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