Some 77 million Mexicans were registered to vote
The once all-powerful Institutional Revolutionary Party (PRI) is set to be the biggest force in Mexico's Congress after success in mid-term elections.
With most results in, the National Action Party (PAN) of President Felipe Calderon conceded that the PRI would be the main party in the lower house.
The PRI dominated Mexican politics for seven decades until 1997.
The election campaign was overshadowed by the severe economic downturn and the government's drive against drug gangs.
"We recognise the election results and congratulate the Institutional Revolutionary Party with becoming the largest party in the Chamber of Deputies," PAN Chairman German Martinez said as results came in from Sunday's elections.
The head of the PRI, Beatriz Paredes, said the result showed that Mexico was looking for "new proposals and new solutions".
The PRI will be the biggest force in the Chamber of Deputies and with allies could muster an absolute majority.
The PRI was also on course to win the governorships in several states, Mexican media reported.
Mexico has been badly hit this year by the global recession and a drop in the amount of money sent home by migrant workers.
The outbreak of swine flu in April has also scared off tourists, which the government has warned may cost the economy more than $2bn (£1.2bn).
Eyes on 2012
Mr Calderon won a bitterly fought presidential election three years ago promising reforms to restore economic growth.
His party had hoped his crackdown on the powerful drug cartels would reap electoral rewards this time round.
"The competition is behind us and now we have to focus on our efforts on seeking the agreements the country needs to recover, as soon as possible, economic growth, job creation and public safety," Mr Calderon said, as he appealed to the new Congress to work together.
The PRI's victory could complicate his efforts to enact major reforms, correspondents say. But analysts also point out that the party is no longer the huge monolith of decades past but composed of often competing factions.
One key element will be the manoeuvring for position ahead of the presidential elections due in 2012.
The PRI controlled Congress until losing its majority 12 years ago. The party's grip on the presidency ended in 2000.
Mexicans were electing 500 members of the Chamber of Deputies, the lower house of Congress, as well as six state governors and hundreds of mayors.