Mexican President Enrique Pena Nieto and his Institutional Revolutionary Party will keep control of Congress, preliminary election results suggest.
The PRI is set to win about 30%, with the conservative National Action Party on about 22%, said the head of the National Electoral Institute.
On current projections, the PRI will see its number of seats drop slightly.
The run-up to the poll was marked by violence with drug cartels blamed for the deaths of several candidates.
On Sunday morning, protesters and parents of 43 students who disappeared last year burned election material in the town of Tixtla.
They say they want answers about what happened to the students before elections are held.
A dissident teachers’ union also burned ballots and ransacked offices of political parties to express its anger at education reforms.
Analysis by Katy Watson, BBC News, Mexico City
Ahead of the elections, there was a great deal of pessimism – the feeling among many that votes do not really matter, politicians here are all the same, and violence will continue no matter what.
But at a polling stations on Sunday, in relatively peaceful Mexico City, there was a sense of duty among many – that voting was the only way to make a difference. Asked what their main concern was and almost without exception, the response among voters was: ‘Security.’ People here are worried about where the country is heading.
Despite President Pena Nieto’s promises to restore peace in Mexico, these elections have proved otherwise. They have been some of the most violent in recent history.
President Pena Nieto deployed federal police and troops to guard polling stations.
His spokesman Eduard Sanchez said on Saturday: “Mexicans have the right to vote in peace… [we] will take all necessary measures within the framework of legality” to protect the elections.
Ahead of the polls opening, the CNTE teachers’ union attacked the offices of five political parties in Chiapas state in the south of the country.
In Guerrero state, explosive devices were thrown into a conservative party’s office.
Meanwhile in Oaxaca, as well as Guerrero, tens of thousands of ballot papers were burnt by protesters.
A former mayor was shot dead outside a polling station in the same state.
A number of candidates and numerous campaign workers have also been killed in drug-related violence.