CARACAS/SAN CRISTOBAL, Venezuela, April 19 (Reuters) - Two Venezuelan students died on Wednesday after being shot during protests against unpopular leftist President Nicolas Maduro, increasing turmoil in the volatile nation amid a brutal economic crisis.

Opposition supporters protested in Caracas and other cities in what they called “the mother of all marches,” denouncing Maduro for eroding democracy and plunging the oil-rich economy into chaos.

Crowds swelled to hundreds of thousands, including Maduro supporters who held a counter-demonstration in the capital at the urging of the president, and clashes were reported across the country during the most sustained protests since 2014.

Maduro says that beneath a peaceful facade, the protests are little more than opposition efforts to foment a coup to end socialism in Venezuela. The opposition says he has morphed into a dictator and accuses his government of using armed civilians to spread violence and fear.

The dueling marches drew parallels to the clashes between pro and anti-government protesters in 2002 that triggered a brief coup against late President Hugo Chavez.

CARLOS BECERRA via Getty Images Opposition demonstrators march against the government of Venezuelan President Nicolas Maduro, in Caracas.

Carlos Moreno, 18, a student, was on his way to play soccer in Caracas and did not plan to take part in the demonstration when government supporters approached an opposition gathering and fired shots, according to witnesses and a family member. He was shot in the head, they said, and three security officials said he later died in a clinic after undergoing surgery.

Later on Wednesday in the opposition hotbed of San Cristobal near the Colombia border, university student Paola Ramirez died after being shot by armed men on motorbikes as she was leaving the protest, relatives and witnesses told Reuters.

The public prosecutor’s office said it was investigating both cases.

The deaths mean seven people have now been killed during protests in Venezuela this month. The opposition blames the deaths on security forces and alleged paramilitary groups.

Waving the country’s red, yellow and blue flags and shouting “No more dictatorship” and “Maduro out,” demonstrators clogged a stretch of the main highway in Caracas. Troops fired tear gas in Caracas neighborhoods, San Cristobal, the depressed industrial city of Puerto Ordaz, and the arid northern city of Punto Fijo.

“We have to protest because this country is dying of hunger said Alexis Mendoza, a 53-year-old administrator marching in the Caracas neighborhood of El Paraiso. “There are a lot of people in the opposition and they are full of courage.”

FEDERICO PARRA via Getty Images Riot police officers confront demonstrators in Caracas.

The march followed a fortnight of violent protests triggered by a Supreme Court decision in March to assume the powers of the opposition-led Congress - which it quickly reversed under international pressure.

The court’s move nonetheless fueled long-simmering anger over the ruling Socialist Party’s handling of the economy. The OPEC country suffers from Soviet-style shortages of food and medicines and triple-digit inflation.

The opposition is demanding early elections, the freeing of jailed politicians, humanitarian aid, and respect for the autonomy of the opposition-led legislature.

The marchers gathered at more than two dozen points around Caracas, although some were stalled by authorities closing around 20 subway stops. Protesters had hoped to converge on the office of the state ombudsman, a guarantor of human rights, but as in previous attempts they were blocked by the National Guard. The protests trailed off with youths throwing rocks squaring off against security forces spraying tear gas.

Carlos Garcia Rawlins / Reuters An opposition demonstrator carries a gas grenade while clashing with riot police during the so called "mother of all marches."

MADURO SAYS “ANTI-CHRISTS” DEFEATED

Maduro has charged that the opposition is trying to relive the 2002 coup against Chavez, his predecessor and mentor, by blocking roads with burning trash and vandalizing public property.

On Wednesday afternoon he addressed a cheering red-shirted crowd in Caracas to declare that a “corrupt and interventionist right-wing” had been defeated.

“Today the people stood by Maduro!” the president said, blasting his rivals as “anti-Christs.” “We’ve triumphed again! Here we are, governing, governing, governing with the people!” he added, before breaking into song.

Analysts say there is less likelihood of a coup against Maduro because Chavez launched a broad purge of the armed forces following his brief ouster.

Some unhappy Venezuelans also steer clear of protests, fearful of violence, cynical that marches can bring about change, or too busy looking for food amid the recession.

Venezuela benefited for years from oil-fueled consumption and many poor citizens rose into the middle class. But the 2014 collapse in oil prices left the government unable to maintain a complex system of subsidies and price controls. Snaking grocery lines are now a common sight and people routinely say they skip meals and cannot find basic medication.

Further spurring outrage was a decision by the national comptroller’s office earlier this month to disqualify opposition leader and two-time presidential candidate Henrique Capriles from holding office for 15 years, dashing his hopes for the presidency.

FEDERICO PARRA via Getty Images Supporters of Venezuelan President Nicolas Maduro take part in a counter-demonstration in Caracas.

The elections council, which is sympathetic to the government, has delayed votes for state governors that were supposed to take place last year. The opposition charges that this is because the Socialist Party would be likely to fare poorly in such a vote.

Eleven Latin American countries issued a joint statement this week calling on authorities to set a time frame for elections to “allow for a quick solution to the crisis that Venezuela is living through.”

Demonstrators also gathered on Wednesday in the eastern city of Puerto Ordaz, home to Venezuela’s struggling state-run mining companies, and the oil city of Maracaibo.

“I’ve just graduated ... and what I’ve got in the bank isn’t enough for a bottle of cooking oil,” said Gregorio Mendoza, a 23-year-old engineer in Puerto Ordaz. “We’re poorer every day.”

(Additional reporting by Eyanir Chinea, Diego Ore, Girish Gupta, and Andreina Aponte in Caracas, German Dam in Ciudad Guayana, Maria Ramirez in Puerto Ordaz, Isaac Urrutia in Maracaibo, Mircely Guanipa in Punto Fijo, and Anggy Polanco in San Cristobal; Writing by Brian Ellsworth and Alexandra Ulmer; Editing by Frances Kerry and Lisa Shumaker)