The clashes erupted when supporters of President Hugo Chavez and the National Guard tried to prevent opposition lawmakers from entering the Capitol building. Chavez's critics countered with shouts of "Democracy!" and "No to dictatorship!"
But defiant lawmakers broke through the crowd and climbed over the fence. Six people were injured.
Chavez's supporters in the assembly tried Wednesday to limit the Congress' powers, banning the opposition-controlled Congress from passing laws. That ban came barely a week after the assembly also gave itself sweeping new judicial powers.
Critics warned that one of Latin America's oldest democracies was in jeopardy.
"I call on the government to respect the right of legislators to convene," said Sen. Cesar Perez Vivas, head of the parliamentary faction of the opposition Copei Party. He added that Chavez and the constitutional assembly were "trying to liquidate" Congress.
Members of the opposition controlled Congress insisted Friday they would meet anyway, despite efforts by Venezuela's Catholic Church to head off a confrontation.
Leaders of both entities, along with several cabinet ministers, were meeting at the Church's headquarters.
Chavez supporters, including his wife, brother and five former ministers, captured 121 of the assembly's seats in national elections last month.
The Supreme Court ruled in April that the assembly's sole mission is to write a new constitution for Venezuela. But at Chavez's behest, the panel has proceeded to intervene in the other branches of government.
The Supreme Court's president, Cecilia Sosa, resigned last week to protest a court ruling supporting an assembly decree giving itself extensive new power to fire judges and overhaul the judicial system.
Chavez, a former paratrooper who led a failed 1992 coup attempt, says a major shakeup of Venezuela's institutions is needed to root out some of the world's worst political corruption.
But his detractors say he is leading Venezuela toward dictatorship.