The United States on Sunday condemned the elections for the National Constituent Assembly (ANC) in Venezuela, claiming the voting "undermines the Venezuelan people's right to self-determination."

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.

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.

The United States has joined Mexico, Colombia and Panama in saying that they would not recognize the voting results.

Elias Jaua, president of Venezuela's Constituent Commission, said that the ANC did not need the recognition of "any government."

A total of 41.53 percent of Venezuelan voters cast their ballots in Sunday's elections, the National Electoral Council told the press.

At least five people were reportedly killed during the voting.