The prosecutor general's office says it will appeal the Supreme Court's decision.
Voters in Sao Paulo re-elected centre-right mayor Bruno Covas for a new four-year term defeating leftist opponent Guilherme Boulos.
After 18 months in prison, Brazil’s former president Luiz Inacio Lula da Silva pledged to bring the country back to the left.
Hundreds of supporters gathered outside the federal police headquarters in the southern city of Curitiba where Lula has been held since April 2018 cheered after the order was issued.
Jair Bolsonaro, a far-right politician vowing a crackdown on crime and corruption, was sworn in as Brazil's new president in front of Congress in Brasilia.
Brazil's top judge Jose Antonio Dias Toffoli ruled that the full court would have to take up the case of former president Luiz Inacio Lula da Silva after it returns from holiday recess.
New investigations against the former presidents could spell longer prison terms for Luiz Inacio Lula da Silva and Dilma Rousseff.
Brazil's former president Luiz Inacio Lula da Silvain stepped aside allowing running mate Fernando Haddad to stand for the presidency in the country's upcoming presidential election scheduled for 7 October.
Right-wing candidate Jair Bolsonaro, who was knifed in the abdomen while campaigning on Thursday, is in serious condition, his son and a hospital spokeswoman confirmed.
Brazil's top electoral court barred jailed former president Luiz Inacio Lula da Silva from running in this year's presidential election because of his corruption conviction.
Lula is the candidate for his Workers Party (PT) and leads presidential polls ahead of the October ballot, but is widely expected to be banned from running by an electoral court. He was jailed in April on a corruption conviction.
Judge Sergio Moro, who sent Lula to prison in April for a bribery conviction, said that the appeals court judge lacked authority to issue an order freeing the former president for campaigning in the run-up to the October vote.
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