Nine protesters were injured, including one who was shot in the leg, said Ramon Muchacho, mayor of one of Caracas's districts. None of the injuries were life-threatening, he said.
Protesters hurled stones at riot police, who fired tear gas as they blocked the demonstrators from advancing along Libertador Avenue through central Caracas, where pro-government activists also marched.
An estimated 1,000 people tried to march to the National Assembly to demand the government restore powers to its opposition majority. Lawmakers were among the marchers.
Among those who felt the sting of the tear gas was the speaker of the National Assembly, Julio Borges, and former presidential candidate Henrique Capriles.
"This is how they show disrespect for people sworn in as lawmakers," Borges said on Twitter. "Lawmakers assaulted on Libertador Avenue as we headed in to hold a session."
Lilian Tintori, wife of jailed opposition leader Leopoldo Lopez, said: "They used tear gas bombs against us. It was like war.
"Venezuela is in the grips of a dictatorship but we are going to free it," Tintori told reporters.
A move by the Supreme Court last week to take over the legislature's powers sparked international condemnation.
The United States and other powers backed the opposition's calls for the government to allow timely elections and release political prisoners.
The court later backtracked on its move, but the opposition pressed ahead with calls for demonstrations.
Opposition lawmakers were preparing to discuss moves to try to fire judges from the court, at a session scheduled in the assembly later Tuesday. But in the end, it was put off until Wednesday.
The center-right opposition wants to remove the socialist president from office, blaming him for an economic crisis that has caused food shortages in the oil-rich nation.
Maduro says the crisis is the result of a capitalist conspiracy. The opposition has urged the military to drop its support for him, but so far he still has the public backing of the high command.
"We want liberty in Venezuela. This is a dictatorship," one protester, 56-year-old nurse Maria Gonzalez, yelled at the police.
"Soon there will be no more food. Is that what you want for your children?"
In the pro-government march, thousands of people denounced a the Organization of American States for criticizing the Venezuelan government over the court move.
"We support Maduro against these attacks, which seek to carry out a coup d'etat," said one demonstrator, Angelo Olivo.
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