"We recognise that the PRI [Institutional Revolutionary Party] will be the main bloc in the new chamber of deputies," German Martinez, the president of the ruling party, PAN, said on Monday.
The dire state of Mexico's economy, which is in deep recession due to the downturn in the US next door, was a critical factor for voters, who turned against Calderon's PAN.
The PRI, which ruled Mexico for 71 years until Vicente Fox, the former president, ousted it in elections in 2000, had a reputation for ruling with a mixture of authoritarianism and corruption.
But Calderon's party has since failed to deliver on promises of jobs and low crime, pushing voters toward the PRI.
Mexico has lost hundreds of thousands of jobs this year and the economy is likely to shrink by more than 6 per cent.
Mixed record
Calderon wants to overhaul the energy sector to allow more private investment in the search for oil in the Gulf of Mexico.
He also seeks to reform the tax system and labor laws.
But he will have to negotiate with the centrist PRI to push reforms through congress.
The PRI has already watered down reform attempts by Calderon, who has lacked a majority in congress since he became president in a tight election in
2006.
Calderon is popular and voters generally support his war against drug cartels. More than 12,300 people have died since he dispatched the army to battle drug gangs three years ago but congress has not played a major role in the fight.
Robberies, kidnappings and muggings are a major concern among voters.
Decades of sluggish economic growth have kept most Mexicans poor and spurred millions of people to cross the US border in search of work.