Venezuela's National Electoral Council said early Sunday that more than 8 million people had voted to grant President Nicolas Maduro's ruling socialist party virtually unlimited powers with a new constitutional assembly -- a turnout more than double the estimates of both the government's political opponents and independent experts.

The U.S. blasted the vote as a "step toward dictatorship," and the Trump administration vowed a "strong and swift" response. CBS News correspondent Manuel Bojorquez reports that the U.S. is vowing to respond to the election with new sanctions against Venezuela -- possibly as soon as Monday.

Electoral Council president Tibisay Lucena announced just before midnight that turnout in Sunday's vote was 41.53 percent, or 8,089,320 people. As Bojorquez reports, not a single opposition member was among the more than 5,000 candidates on the ballots to fill the new constitutional assembly. The new 545-member body will have sweeping powers to rewrite Venezuela's national charter.

That count was met with mockery and anger from members of the opposition, who said they believed between 2 million and 3 million people voted. One well-respected independent analysis said 3.6 million appeared to have voted.

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The electoral council's vote counts in the past have traditionally been seen as reliable and generally accurate, but Sunday's announcement appeared certain to escalate the polarization and political conflict paralyzing the country.

Venezuelan President Nicolas Maduro has provoked international criticism and enraged his political opponents by pushing for the special assembly to rewrite the troubled South American nation's constitution.

Sunday's election of delegates to the assembly comes after nearly four months of political upheaval that have resulted in more than 100 deaths and left thousands injured and detained.

Protesters like Juan Carlos Gutierrez tell CBS News they were threatened with 10 years in jail if caught marching in the streets.

"We have a little piece of democracy and they kill it -- the government is killing it," he said.

The U.S. State Department officially condemned the Venezuelan government for holding the vote, calling it a step toward authoritarian rule. In a statement released Sunday night, the State Department said the new body seemed designed to "undermine the Venezuelan people's right to self-determination."

Maduro’s sham election is another step toward dictatorship. We won't accept an illegit govt. The Venezuelan ppl & democracy will prevail. — Nikki Haley (@nikkihaley) July 30, 2017

The U.S. had already joined Argentina, Peru, Colombia, Panama and in a late Sunday night addition, Mexico, in saying it would not recognize the vote results. U.S. Ambassador to the United Nations Nikki Haley tweeted earlier Sunday that the vote was a "sham election" which takes Venezuela "another step toward dictatorship."

The State Department said Washington would "continue to take strong and swift actions against the architects of authoritarianism in Venezuela."

While the U.S. hasn't said specifically what any new sanctions against Venezuela will target, oil accounts for nearly half of the government's revenue, and Venezuela is the third-largest supplier of oil to the U.S., which buys about a third of the country's crude. Falling oil prices, coupled with sky-rocketng inflation, have already crippled Venezuela's economy.

With the protests still raging, Venezuela's chief prosecutor's office reported three deaths on the day of a controversial vote. The office tweeted that 28-year-old Angelo Mendez and 39-year-old Eduardo Olave were killed at a protest Sunday in Merida. Thirty-year-old Ricardo Campos was killed in a separate incident in Sucre.

Few details were provided on the deaths.

Leaders with the opposition Democratic Action party on Twitter identified Campos as the group's youth secretary in Sucre, a state in northern Venezuela east of the nation's capital.

The deaths bring the total to at least 122 killed in nearly four months of political upheaval.

Even Maduro's own vote in the election he had called turned into a lightning rod for his critics, as he appeared -- with state television cameras rolling -- to be unregistered to vote in his country.

When Maduro cast his, his national ID card was scanned by a National Electoral Council (CNE) employee just like all other voters. But when the CNE official used a smartphone to scan Maduro's card, a second camera zoomed in to reveal that, according to CNE's own system, Maduro's national identity "number does not exist, or the card has been revoked."

After scanning President Nicolas Maduro's national ID card, the smartphone read: "number does not exist, or the card has been revoked." Reuters

Maduro appeared livid, but didn't overtly acknowledge the misshap. He paused briefly before grabbing his wife's ID card and having that scanned and casting his vote.

The gaffe set Venezuelan social media abuzz, and fanned the flames of speculation about the socialist president's place of birth; his whose mother is rumored to be a Colombian national. Following an opposition-mandated special commission investigation into the matter, the socialist-majority Supreme Court issued a ruling last October that stated that Maduro had been born in Caracas in 1962, but did not produce a birth certificate.

Some opposition leaders continue to insist they have proof that Maduro was born a Colombian national, which would make him constitutionally ineligible to hold the presidency.

Few specifics have been disclosed on what constitutional changes might be in store under the new constitutional assembly, but Maduro allies have said it will target opposition leaders, stirring warnings that Maduro will use the assembly to install an autocratic regime.

Maduro's mentor, the late President Hugo Chavez, similarly called for a constitution rewrite shortly after taking office in 1999, but unlike Maduro he held a referendum first to get Venezuelans' blessing. Even some "Chavistas" have rejected the drive to change the constitution, which has further polarized an already deeply divided country.