Anaya campaigns with the coalition of the conservative National Action Party and the left-wing Party of the Democratic Revolution. He now ranks second among the candidates, according to pre-election polls.
"The Mexico we dream of is one in which there is no corruption, where the government behaves with honesty," Anaya said before thousands of supporters at his final rally in Mexico city on Sunday.
"The Mexico we dream of is also one in which no one lives in extreme poverty," he added.
Anaya is chasing Andres Manuel Lopez Obrador, a left-wing candidate and former mayor of Mexico City. Polls show Lopez Obrador has consolidated his lead. Jose Antonio Meade of the Institutional Revolutionary Party is third in place while independent candidate Jaime "El Bronco" Rodriguez is the fourth in line. Some 89 million eligible voters will choose a successor to President Enrique Pena Nieto on July 1. Also up for election are the governors of eight states and the capital Mexico City, and 500 federal deputies and 128 senators, as well as mayors and local legislators.