Before Sunday's vote, President Enrique Pena Nieto's Institutional Revolutionary Party (PRI) held nine of the 12 states at play. There are 32 federal regions in Mexico.
But preliminary results showed that it was leading in just five states and losing two key bastions, Tamaulipas and Veracruz, both of which it has controlled for more than 80 years.
The biggest winner was the conservative National Action Party (PAN), which was ahead in seven states, including three in partnership with the leftist Democratic Revolution Party (PRD).
"If we do things right, if we follow through, if we show results in those states, the PAN will reclaim the presidency in 2018," Anaya said.
The PAN ended the PRI's 71-year hold on the presidency in 2000, but Pena Nieto returned his party to power in 2012.
The president, however, has since seen his popularity sink to 30 percent, with Mexicans unhappy at his handling of the economy, corruption and drug violence.
PRI leader Manlio Fabio Beltrones said the results show that his party must take action to "reconnect with citizens.
