"My absolute condemnation of the assault on the democratic institutions of Brazil," European Council President Charles Michel wrote on Twitter.
"Full support for President @LulaOficial Da Silva, democratically elected by millions of Brazilians through fair and free elections," he added, referring to President Luiz Inacio Lula da Silva.
The bloc's foreign policy chief Josep Borrell said he was "appalled by the acts of violence and illegal occupation" carried out by "violent extremists" in the Brazilian capital Brasilia.
"Full support to @LulaOfficial and his government, to Congress and to the Federal Supreme Court. Brazilian democracy will prevail over violence and extremism," he said on Twitter.
"The place to resolve political differences is within Brazil's democratic institutions and not through violence on the streets," he added.
European Parliament President Roberta Metsola tweeted in Portuguese: "Deeply concerned about what is happening in #Brazil. Democracy must always be respected."
Lula narrowly won October's presidential election in a second-round run-off, scoring 50.9 percent to Bolsonaro's 49.1 percent.