Huge rallies have been held in several Mexican cities against what protesters say are government attempts to undermine the electoral authorities.

The biggest was in Mexico City, where organisers say 500,000 people marched on the city's main plaza. The local government put the number at 90,000.

Lawmakers last week voted to slash the budget of the National Electoral Institute (INE) and cut its staffing.

President Andrés Manuel López Obrador accuses the INE of being partisan.

But opponents describe the recent vote as an attack on democracy itself, pressing the Supreme Court to overturn them as unconstitutional.

On Sunday, massive crowds gathered in Mexico City's historic Zocalo Square. The demonstrators spilled out into adjoining streets in the city centre.

"We're fighting to defend our democracy," protester Veronica Echevarria was quoted as saying by Reuters. She was wearing a cap emblazoned with the words "Hands off the INE". Many demonstrators carried cards with a similar slogan.

Smaller peaceful demonstrations were staged in several other cities.