Venezuela's National Electoral Council said more than 8 million people voted to elect a new National Constituent Assembly (ANC) tasked to rewrite the constitution, with a 41.53-percent turnout rate.

The turnout is far beyond the estimates by both the government's political opponents and independent experts. The opposition said they believed some 2 million people voted.

President of the electoral body Tibisay Lucena announced at a press conference just before midnight that 8,089,320 people cast their ballots in the election.

Tensions bubbled over into violence on Sunday as police cracked down on violent protesters of the election, causing at least 10 deaths across the country, according to Venezuela's chief prosecutor's office.

Foreign Minister Samuel Moncada, however, said the strong participation of Venezuelans in Sunday's ANC election is a "vote for peace."

"Opponents, some governments and even the CIA do not recognize this power ... because they have a plan to control Venezuela. We do not need them or the vote of opponents," said Moncada, calling the election a "declaration of sovereignty."

The governments of Argentina, Britain, Colombia, Mexico, Panama and the United States, among others, have said they would not recognize the results of the election.

The voting in Venezuela was a "flawed" one "designed to replace the legitimately elected National Assembly," the U.S. State Department said in a statement released Sunday night, claiming the voting "undermines the Venezuelan people's right to self-determination."

The United States will "continue to take strong and swift actions against the architects of authoritarianism in Venezuela," including those who participate in the ANC, said State Department spokeswoman Heather Nauert.

Polls opened early Sunday morning in Venezuela to elect 537 of the total 545 members of the ANC with the remaining eight seats belonging to the indigenous people.

The ANC was proposed by President Nicolas Maduro in May to rewrite the 1999 Constitution to break the ongoing political deadlock that has paralyzed the South American country. But the opposition says it is an excuse for Maduro to consolidate power.