By Andrew Cawthorne and Eyanir Chinea

CARACAS (Reuters) - Venezuela's opposition vowed on Monday to revive the OPEC nation's troubled economy and free jailed political activists after winning control of the legislature for the first time in 16 years of Socialist rule.

By afternoon, some results from Sunday's election were not yet in, but the Democratic Unity coalition had already won a commanding majority in the 167-member National Assembly.

Opposition leaders said final tallies showed they reached the crucial bar of two-thirds. There was no confirmation of that from the election board, which still has 22 seats to announce.

If they have reached two-thirds, or at least 112 seats, the opposition could flex its muscles far more against President Nicolas Maduro, by shaking up institutions such as the courts and election board widely viewed by Venezuelans as pro-government.

The 53-year-old Maduro, handpicked by Chavez but lacking his charisma and political guile, quickly accepted defeat in a speech to the nation in the early hours of Monday that calmed fears of violence in a country long riven by political strife.

After securing the assembly from the "Chavismo" movement, named for late former socialist President Hugo Chavez, the opposition quickly set out its priorities.

"It's a great opportunity for us, this protest vote," prominent opposition leader Henrique Capriles said following a win attributed largely to voters punishing the Socialists for Venezuela's deep economic and social crisis.

Coalition head Jesus Torrealba said the opposition would seek to modify the Central Bank law, in an effort to reduce indiscriminate printing of money that has driven the world's highest rate of inflation.

Though it will not have the power to radically overhaul the economy from the legislature, the opposition is also promising new laws to stimulate the private sector and to roll back nationalizations.

The opposition also wants to pass an amnesty law for jailed opponents of Maduro when the new assembly begins work on Jan. 5.

Venezuela's best-known jailed politician is Leopoldo Lopez, who was sentenced to nearly 14 years on charges of promoting political violence in 2014 that killed 43 people. But the opposition has a list of what it says are more than 70 other political prisoners.

BONDS RISE

Investors reacted positively to the OPEC nation's swing away from the left, with dollar bonds rising strongly on hopes of business-friendly change.

On the official count by the election board, the opposition had 99 seats to the Socialists' 46, with 22 seats yet to be announced. The opposition can now exercise control over the budget, begin investigations that could embarrass the government, and fire ministers.

Torrealba has also said the assembly will open an investigation into the arrest last month of two relatives of Maduro, nephews of his wife, caught in a sting in Haiti and indicted in a New York court on charges of cocaine smuggling.

The United States, which has had an acrimonious relationship with Venezuela under both Chavez and Maduro, has long accused the Socialists of complicity in the drug trade, as well as human rights abuses.

The government dismisses those charges as lies and frequently recalls U.S. support for a short-lived 2002 coup against Chavez.

Secretary of State John Kerry said the vote showed Venezuelans' "overwhelming desire" for change and urged dialogue among political parties to resolve the country's problems.

A former bus driver and foreign minister who narrowly won election in 2013 after Chavez died from cancer, Maduro may face a backlash in the ruling party and from grassroots supporters who think he has betrayed his predecessor's legacy.

Although his term ends in 2019, hardline opposition leaders want to oust him in a recall referendum next year. They would require nearly 4 million signatures to force the recall vote.

"I can't see this government finishing its term because it is too weak," said opposition leader Henry Ramos, touted as a possible leader for the new assembly. "Internal frictions are beginning. They're blaming each other for this huge defeat."

'COUNTER-REVOLUTION'

Maduro, whose government has replaced Cuba as Latin America's most vocal adversary of the United States, blamed the election on an "economic war" waged by business leaders and other opponents out to sabotage the economy and bring him down.

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