"The plenary of the Supreme Court considers that imprisonment based exclusively on a criminal conviction can only take place after all the possibilities of appeal (res judicata) have been finalized", the message said.
Lula's lawyers say they will seek the former president's "immediate release" after speaking to him on Friday.
Though Lula's release could galvanize the left and stir up an already heated political environment, it would have small repercussions on Brazil's economic reforms, according to consultancy Eurasia.
Da Silva once led the union, which served as the base for his political career.
The compound was decorated with a huge banner of Lula's image and surrounded by a sea of supporters wearing red T-shirts and waving "Free Lula" flags.
On the same day, the Supreme Court chose to end mandatory imprisonment for convicted criminals after they lose their first appeal, which led to the release of dozens of high-profile convicts, including Lula.
Lula had already appealed his conviction but it was upheld previous year, and he was put behind bars in April 2018.
"He (Bolsonaro) was elected to govern for the Brazilian people and not to govern for the militias in Rio de Janeiro", said Lula, his face flushed as he ranted for almost an hour in the heat.
Granit Xhaka stripped of the Arsenal captaincy following Emirates outburst
Unai Emery took his time in officially unveiling Granit Xhaka as the Gunners' skipper, only for the midfielder to be stripped of the armband this week.
"People are hungrier, they have no jobs, people work for Uber or delivering pizzas on a bike", Lula said in remarks sometimes drowned out by cheers from the crowd and fireworks overhead. Lula was expected to run for president again in 2018 before being imprisoned, and was still featured heavily in ads for the campaign of the candidate of his Workers' Party, Fernando Haddad, who lost to Bolsonaro.
Earlier, he had posted "Lula Free" on social media, along with a video of himself working out and lifting weights in a gym.
The 74-year-old leftist icon embroiled in a massive corruption scandal which has engulfed some of Brazil's most influential politicians and business leaders.
The ruling additionally covers other people convicted in instances arising from the so-known as Auto Wash investigation, which has ensnared dozens of greatest politicians and group leaders in Latin America's best nation.
Da Silva has denied any wrongdoing and accuses Car Wash prosecutors and then-judge Sergio Moro, now Justice Minister, of political persecution.
Brazil has a four-level appeal system, while the former president has only gone through two of them.
Da Silva, who governed from 2003 to 2010, had been favored to win the 2018 presidential election, but his conviction prohibited him from running.
In a separate Supreme Court debate, justices will decide whether Moro was biased when he delivered his rulings.