Mexican President Claudia Sheinbaum hit back Monday at criticism of her country's unprecedented election of judges, after most voters skipped a ballot that her opponents called a farce.

Sunday's election followed highly contentious reforms making Mexico the only country in the world to let voters select all of their judges, including Supreme Court justices.

As officials began the long process of tallying votes, Sheinbaum hailed the "complete success" of an exercise she said was needed to clean up a judiciary mired in corruption.

The National Electoral Institute said around 13 percent of eligible voters took part in a poll that critics said would erode democratic checks and balances and leave judges more vulnerable to criminal influence.

The low participation rate compared with turnout of around 60 percent in presidential elections last year that Sheinbaum won by a landslide.

The veteran left-winger told Mexicans after the election they have "nothing to fear."

"Mexico is a free, democratic country -- that won't change. Nothing will change, except access to justice," she said.

Sheinbaum pushed back at claims "that we're heading toward authoritarianism and that the president will have a lot of power because she'll control the judiciary."

The leader of the opposition Institutional Revolutionary Party, Alejandro Moreno, denounced the vote as a "farce" and called it a "dark day for democracy."

"They weaken the justice system, trample on institutions, and block the way to democratic debate," he said.

Many voters seemed daunted by the long list of largely unknown candidates in an election for around 880 federal judges as well as hundreds of local judges and magistrates.

Another election for the remainder will be held in 2027. (AFP)