Supporters and opponents of Venezuela's leftist government staged rival rallies Saturday in Caracas that took place amid protests and spiraling discontent at the country's stubborn inflation and basic goods shortages.

About 3,000 opponents dressed in white and carrying red, blue and yellow Venezuelan flags gathered in an affluent area of the capital, fanning out into nearby streets, just days after demonstrations left three people dead.

The protesters, mostly students, have spearheaded nearly two weeks of marches against President Nicolas Maduro, angered by rampant crime, rising prices and a lack of essential supplies as basic as toilet paper in a nation that sits on top of the world's largest proven oil reserves.

On Saturday the demonstrators demanded the release of about 100 detained students and other opposition activists, and an end to police repression, but at least one protest ended with police officers firing tear gas.

The depth of the unrest on what is now the 12th day of street protests was underscored by Maduro's decision to address a counter-rally, and by US Secretary of State John Kerry voicing alarm at the reported arrests.

But speaking before thousands of supporters gathered in downtown Caracas, Maduro accused conservative Colombian ex-president Alvaro Uribe, whom he regards as a US ally and foe of Venezuela, of "funding and directing" the "fascist movements" he blames for the unrest.

Maduro's elected socialist government has also taken Colombian news channel NTN24 off the air, saying it was inciting anti-government violence.

Protests have taken place in different cities in Latin America, and on Saturday, dozens of activists, many of them youths, rallied in front of the Venezuelan Embassy in Washington.

They carried banners reading "SOS Venezuela," "We say no to dictatorship" and "Venezuela is not alone." Many wore clothing in the colors of the Venezuelan flag.

A handful of pro-government protesters held banners at the embassy gates that read "We are with the Bolivarian revolution."

Top US diplomat Kerry said in a statement that reports of Venezuela's leaders arresting scores of anti-government protesters would "have a chilling effect on citizens' rights to express their grievances peacefully," and he called for all parties to work together to resolve tensions.

- Crackdown after violence -

Two anti-government protesters and a pro-Maduro demonstrator died in a rally Wednesday, in violence that raised alarm throughout Latin America and also in Europe. Some 60 people were also injured.

"Before, we would not go out on the street because of violent crime. Now, we go out to protest -- and they kill us," said university student Isaac Castillo, 27.

"We young people have no faith, no hope. There are no jobs and even if we get one, it is not enough to make a decent living."

In downtown Caracas, government supporters wearing the bright red symbolizing the leftist movement of the late Hugo Chavez and Maduro, his handpicked successor, filled several plazas.

Some protesters danced or did aerobic exercises to the rhythmic beating of drums played by their fellow demonstrators.

And other demonstrators unfurled huge Venezuelan flags and pictures of South American liberation hero Simon Bolivar and of Chavez.

Maduro says the protests against him signal the rumblings of a coup to depose him, vowing to use force to prevent unauthorized street gatherings.

The president has accused opposition leader Leopoldo Lopez of being one of the main backers of the protests, and he is wanted for arrest.

The latest anti-government movement, backed by some of the country's fractured opposition groups, poses the biggest challenge to Maduro since 2013 election, held after Chavez died of cancer.

A nationwide security crackdown has followed the violence in a country where the economy has been battered by inflation of more than 50 percent.

Seeking to quell the unrest, Maduro unveiled a 10-point plan to crack down on crime that includes disarming the population, increased police patrols and unspecified "clear rules for television."

The protesters have demanded that Maduro step down, although opposition leaders have not endorsed the request.

Despite having oil wealth, Venezuela has severe economic problems and a deep divide between rich and poor.

And with an institutionally socialist government dependent on oil revenues in a state-led system, the nation has been hurt by a shortage of hard currency, while dwindling supplies of consumer goods have frustrated even some government supporters.