The outcome will determine if President Vicente Fox can go ahead with reform plans he promised to carry out when he was elected three years ago.
His rise to power in July 2000 brought an end to 71 years of one-party rule in historic presidential elections.
His economic reform plans have always been blocked by congress members of the opposition Institutional Revolutionary Party (PRI), which had stayed in power for seven decades.
Fox’s National Action Party (PAN) has now 202 out of 500 seats in the Chamber of Deputies.
But the PRI is the largest party in the congress with 207 seats that are enough to block measures they dislike.
The country’s third party, Party of the Democratic Revolution (PRD), a leftist, could gain more seats than the 56 that it now holds, according to polls.
The opinion surveys show that PAN and PRI are running neck-to-neck into the election.
But more than half of Mexico’s 64 million registered voters are expected to abstain from casting ballots, according to the polls.
Fox addresses people
On Saturday, Fox urged Mexicans to vote in comments he made on his weekly radio address.
“This is an opportunity for our voice to be heard, and for every Mexican to choose the direction that we want to give the country,” he said.
“We have struggled generation after generation for our vote to
count, and now we can say that it is the foundation of the democracy in which we live,” he added.
The president also asked people to be patient, saying: “The US economy, the European and Japanese economies, are truly stagnant and this prevents our economy from being able to grow via exports as it has done in the last 10 years.”
Fox, 61, gained credit in his country when he resisted US pressure in the UN Security Council and opposed the Iraq war.
He has also made progress in combating corruption and drug trafficking.