The demonstrations come at a time of growing political tension in Venezuela.
Three people were killed during anti-government protests on Wednesday, and some 100 students were arrested.
President Nicolas Maduro accused the opposition of stirring up trouble as part of a coup plot and urged his supporters to march for peace on Saturday.
Government supporters began arriving at Venezuela Square, in central Caracas, in the morning.
They were dressed predominantly in red or in Venezuela’s national colors – blue, yellow and red.
Hours later Nicolas Maduro addressed thousands of his supporters in Bolivar Avenue. The march was broadcast live on national television.
“I call all the people to the streets in order to defend peace,” he said.
Nicolas Maduro warned that his government would not give in to those he described as “fascists,” including former president of neighboring Colombia, Alvaro Uribe.
“Alvaro Uribe is behind this, financing and directing these fascist movements.”
“He intended to use a Venezuelan television channel [NTN24] to do the same they did on 11 April 2002,” Nicolas Maduro said, referring to a failed military coup against the late President, Hugo Chavez.
Alvaro Uribe, a centre-right politician, was a fierce enemy of Hugo Chavez and accused the late president of supporting Colombia’s largest rebel group, the Farc.
Nicolas Maduro said police had been looking for opposition leader Leopoldo Lopez, accused of ordering “all these violent kids, which he trained, to destroy half of Caracas to then go into hiding”.
Leopoldo Lopez has not been seen in public since an arrest warrant was issued for him on Wednesday.
US Secretary of State John Kerry has issued a statement expressing concern by the rising tensions in Venezuela.
Opposition demonstrators, including a movement known as Mothers in White, gathered at Las Mercedes neighborhood in eastern Caracas.
Thousands of people, mostly wearing white, marched towards the Courts of Justice building and stopped for a memorial ceremony to the three demonstrators killed on Wednesday: Bassil da Costa, Juan Montoya and Robert Redman.
Student leader Enrique Altimari said the main aim of their “peaceful protest” was to “pay tribute to the victims”.
He said the march would end before night fell, to avoid a repeat of the incidents of Wednesday.
The three victims were shot dead by unknown gunmen as the opposition marches came to an end.
The opposition march ended before dusk with clashes between police, who fired tear gas in attempts to disperse the crowd, and demonstrators who hurled stones.
Reports say three people were injured.
The main opposition grievances are high inflation, crime and the shortage of some staples.
Venezuela’s government has blamed the shortages on “saboteurs” and “profit-hungry corrupt businessmen”.
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