Anderson Torres was sacked after supporters of ex-President Jair Bolsonaro stormed Congress, the presidential palace and the Supreme Court in Brasilia.
He was accused on Tuesday of leaving the security forces without leadership but has denied playing any part in the riots.
Thousands of protesters, some clad in yellow Brazil football shirts and waving flags, overrun police and ransack the heart of the Brazilian state.
Brazil’s Federal Police have arrested around 1,500 people but on Tuesday released nearly 600 people mothers of young children, seniors over 65 and others with illnesses accused of participating in Sunday’s anti-democratic acts. They said it was on humanitarean grounds.
On Tuesday, the federal intervenor in public security accused Mr Torres of “a structured sabotage operation”.
The attorney general’s office said it had asked the Supreme Court to issue arrest warrants for Mr Torres “and all other public officials responsible for acts and omissions” leading to the unrest.
Mr Torres, who previously served as Bolsonaro’s justice minister, was fired from his role as Secretary of Public Security on Sunday by Brasília governor Ibaneis Roch.
Ricardo Cappelli, who has been appointed to run security in Brasília, said there was a “lack of command” from Mr Torres before government buildings were stormed.
Lula’s inauguration on January 1 was “an extremely successful security operation,” Mr Cappelli told CNN.
What changed before Sunday was that, on 2 January, “Anderson Torres took over as Secretary of Security, dismissed the entire command and travelled”, he said.
“If this isn’t sabotage, I don’t know what is,” Mr Cappelli added.
Mr Torres that he deeply regretted the “absurd hypotheses” that he played any part in the riots.
He said the scenes, which occurred during his family holiday, were lamentable and said it was “the most bitter day” of his personal and professional life.
Lula has accused security forces of “neglecting” their duty in not halting the “terrorist acts” in Brasília.
Mr Bolsonaro, who has condemned the riots, has not admitted defeat from October’s election that showed deep divisions in the nation.
He flew to the US before the handover on 1 January and on Monday he was admitted to hospital in Florida with abdominal pain.
Lula has accused the security forces of “incompetence, bad faith or malice” for failing to stop demonstrators accessing Congress.