The opposition won at least 99 seats in the 167-seat legislature, National Electoral Council President Tibisay Lucena announced after midnight. The socialist party won 46 seats and the remaining races have not yet been decided.
The streets of the Venezuelan capital of Caracas broke out in shouts of joy and fireworks after the partial results were announced. Opposition leaders had earlier claimed they won but gave no indication of the margin.
But he recalled the long history of coups in Latin America and blamed what he called a "circumstantial" loss on opponents he said have been conspiring to destabilise his socialist revolution.
"I can say today that the economic war has triumphed," Maduro said in a televised address from the presidential palace.
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Former presidential candidate Henrique Capriles said on Twitter that "with great humility, serenity and maturity we accept what the people decided."
It was also a major blow to Latin America's left, which gained power in the wake of Chavez's ascent but more recently has been struggling in the face of a region-wide economic slowdown and voter fatigue in some countries with rampant corruption.
Last month, Argentines elected a conservative businessman over the chosen successor of Cristina Fernandez, who was a close ally of Chavez.
Maduro had repeatedly vowed in recent weeks to take to the streets and defend the socialist system build by his mentor Chavez if his party lost, though yesterday, he appeared to soften his tone.