Thousand of anti-government students lie on the ground during a protest in front of the Venezuelan Judiciary building in Caracas on Feb. 15, 2014. Leo Ramirez/AFP/Getty Images

Thousands of supporters of Venezuelan President Nicolas Maduro marched in central Caracas Saturday to call for peace and make a show of political strength after this week's opposition street protests and ensuing deadly violence.

But in a prosperous eastern part of the capital opposition protests continued undaunted, with at least 1,000 protesters gathered to demand the president's resignation, denouncing him over grievances ranging from political repression to daily issues such as inflation, shortages of basic products and rampant crime.

Almost a year after succeeding the late Hugo Chavez, Maduro accuses his rivals of stoking unrest to try to stage a coup like the one 12 years ago that briefly ousted Chavez. There are, however, no indications the current turmoil could lead to his ouster.

"You want to see people in the streets? We'll give you people in the streets," the president said to loud applause and cheers of "No to fascism!" at the rally.

Addressing the crowd from a pastel-colored stage displaying the slogan "People of Peace," he mocked the demands of protesters who want him to step down.

"I'm not going to give up one millimeter of the power the Venezuelan people have given me ... nothing will stop me from building this revolution which commandant Chavez left us!"

In reaction to the situation in the country, the United States urged all parties to refrain from violence but issued a stern call for the Venezuelan government to ease up its crackdown on the opposition and ensure democratic standards and a respect for human rights.

"We are particularly alarmed by reports that the Venezuelan government has arrested or detained scores of anti-government protesters," Secretary of State John Kerry said in a statement.

"These actions have a chilling effect on citizens' rights to express their grievances peacefully," he said.

On Friday, police used teargas and water cannons to clear some 1,000 protesters from Altamira Square in eastern Caracas, where some of them had lit trash bonfires and blocked streets.

The protesters are vowing to defy Maduro's ban on unauthorized demonstrations, put in place after three people were shot dead this week after an opposition-led march.

On Saturday, supporters of the opposition gathered again to sing and chant slogans in the square. Many then set off to block a major highway, as they had done briefly the night before.

Maduro said in his speech that he had ordered the temporary closure of Metro stations and suspension of bus services in the east of the city, where the protests are centered.

The protesters blame Maduro for a host of complaints ranging from the fast-rising cost of living, shortages of basic products in stores and one of the highest murder rates in the world.

Demonstrations that end in bloodshed could, however, play into the president's hands by helping him unite factions within the ruling Socialist Party, divide the opposition coalition where many question the wisdom of the street tactics – and distract people from economic problems.

Venezuela's state prosecutor said 25 of 99 people arrested in connection with this week's violence had been freed pending trial, and that the others would be processed within hours.

Maduro supporters say he is the victim of Western "imperial" propaganda and saboteurs seeking to discredit Chavez's legacy.

But Maduro's critics say he is wrecking the economy by sticking with failed Chavez-era policies such as currency and price controls, which many local economists blame for the shortages.

Among those critics is hardline opposition leader Leopoldo Lopez, whom the government calls the "face of fascism" and the intellectual author of the violence.

Maduro said Saturday that police were looking for Lopez, acting on a warrant issued to apprehend the Harvard-educated opposition leader.

Lopez remains in his home in the Chacao district of eastern Caracas where he was once mayor, colleagues said, despite a judge's arrest warrant for him.

"The opposition organizes these violent groups, and then they hide and cry," Maduro said during his speech. "You fugitive from justice, trembling with fear, you fascist coward! Hand yourself in!"

Al Jazeera and wire services