The Ministry of Public Security estimated about 18,000 students, housewives, workers and members of the National Regeneration Movement marched Saturday from the Angel of Independence to the Zocalo, Mexican newspaper La Jordana reported.
The protesters shouted out slogans against Pena and his Institutional Revolutionary Party, including "Mexico without PRI," "Mexico voted and Pena did not win," "If taxation, there will be revolution" and "Out Pena, Pena out," the newspaper reported
One protester, identified only as Quiroz, said he decided to march because the vote was not clear.
"There was too much vote-buying ... so obvious ... but you can not legally prove the law is one-sided," he said.
There were demonstrations in seven other Mexican states, including Jalisco, Tamaulipas, Veracruz, Morelos, Quintana Roo, Chiapas and Coahuila, El Universal reported.
Protesters in Cancun were stopped by police when they entered the hotel zone, "a violation of the municipal side," Council General Secretary Eduardo Galaviz said.