CARACAS (AFP) - Opponents of Venezuelan President Nicolas Maduro claimed to have mobilised a million demonstrators on Thursday (Sept 1) in the biggest rally in decades, demanding a referendum on removing him from power.

Police deployed in their hundreds to keep apart anti-government protesters angry at food and medicine shortages from Maduro's supporters who vowed to defend his "socialist revolution."

The rallies raised fears of violence in the oil-rich South American state, where anti-government protests in 2014 led to clashes with police that left 43 people dead.

The leader of the opposition Democratic Unity Roundtable, Jesus Torrealba, told AFP it was the "biggest rally in recent decades" with "between 950,000 and 1.1 million people" taking part.

Demonstrators dressed in white marched in the east of the capital, yelling "Venezuela is hungry" and "This government is going to fall."

"We either come out to march or we will die of hunger. We are no longer afraid of the government," said one demonstrator, Ana Gonzalez, 53.

The rallies come at a highly volatile time for Venezuela, where a plunge in prices for oil exports has caused shortages, violent crime and outbreaks of looting.

"This is a historic march. Today begins a definitive stage in this struggle," Torrealba said.

Thousands of Maduro supporters in red t-shirts and caps, meanwhile, rallied in the central Plaza Bolivar yelling to their leader: "The people are with you."

Maduro estimated his supporters' turnout at up to 30,000.

"Today, we have defeated a coup d'etat," he told the crowd. "They have failed once again. The victory is ours."

The opposition blames Maduro for the economic crisis and wants a referendum on removing him from power. He has branded the effort a right-wing "coup."

"We are here at the call of our president, to defend the revolution," said 37-year-old housewife Carolina Aponte at the pro-government rally.

The authorities arrested three opposition leaders in the days ahead of the march. Senior opposition figure Henrique Capriles said on Thursday that two mayors had also been arrested.

No major clashes were reported during Thursday's marches, which finished in the mid-afternoon, though riot cops faced off with small groups of protesters.

The MUD said in a statement it would hold two further nationwide demonstrations: at electoral offices on Sept 7, and a "national mobilisation day" on Sept 14.

The referendum's timing lies at the heart of the battle.

If it takes place before Jan 10 and Maduro loses, new elections must be held. If he loses in a recall after that date, he would simply hand power to his hand-picked vice president.

The polling firm Venebarometro says 64 per cent of the electorate would vote against Maduro. A study by another pollster, Datanalisis, indicated eight out of 10 Venezuelans want a change of government.

Maduro blames the crisis on the collapse of oil prices and an "economic war" by businesses backed by US "imperialism."

He faces deep public discontent over shortages of basic goods and an inflation rate projected to hit 720 per cent this year.

Analysts have warned of a repeat of the deadly 2014 clashes that left numerous opposition leaders in prison.

Maduro said Thursday he had prepared a decree to strip lawmakers in the National Assembly of their immunity. He accused the opposition speaker of the legislature, Henry Ramos Allup, of inciting violence.

The opposition "cannot be intimidated," Ramos retorted.

"President Maduro, look at all these people who have poured into the streets of Caracas," he said.

"Never has there been such a big peaceful demonstration in Venezuela, without a single act of violence."