The opposition said it would work to release jailed opposition leaders and address the country’s economic crisis.
Nicolas Maduro has announced a cabinet reshuffle but vowed to veto any amnesty law for jailed politicians.
The election result is the worst for the Socialist movement founded by late leader Hugo Chavez in 1999.
The majority means the Democratic Unity coalition can now make sweeping changes, including calling a possible referendum on Nicolas Maduro’s leadership.
It also wants the release of one of its leaders, Leopoldo Lopez, who was given a 13-year prison sentence for inciting violence – a charge critics say was politically motivated.
However, in a TV address, President Nicolas Maduro said he would block any amnesty law: “The murderers have to be prosecuted and have to pay.”
Nicolas Maduro said his Socialist Party would hold an “extraordinary congress” to find out what went wrong at the election.
The opposition meanwhile warned of looming food shortages for Venezuelans.
“We urge the government to stop crying and start working,” opposition leader Jesus Torrealba said.
“We’re just a few weeks away from a very serious problem in terms of food,” he added.
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