A Supreme Court judge announced Friday that Bolsonaro will be included in an investigation into the origins of the sacking, which was sparked by anger at the far-right leader's election defeat to President Luiz Inacio Lula da Silva.
Torres was wanted under a Supreme Court warrant for alleged "collusion" with the rioters, and stands accused of "omission" in his most recent job as security chief for the capital.
The new justice minister Flavio Dino said Friday that authorities would give his predecessor until Monday to return to Brazil, or face extradition.
Dino also confirmed the discovery at Torres' home of a draft decree proposing emergency steps for the possible "correction" of the October election, which Lula won by a razor-thin margin.
The undated and unsigned draft bears Bolsonaro's name at the bottom, but Dino said the authorship was unknown.
Torres said on Twitter the document was "likely" part of a pile of papers that were destined to be destroyed.
He said the contents of the draft had been taken "out of context" to "feed false narratives" against him.
Bolsonaro came under investigation Friday at the request of the office of the prosecutor general (PGR), which cited a video Bolsonaro had posted "questioning the regularity of the 2022 presidential elections."
By doing so, "Bolsonaro would have publicly incited the commission of a crime," the PGR said in a statement.
The Bolsonaro video was posted online two days after the violent storming of the presidency, Congress and Supreme Court but later deleted.
The PGR explained that even though the video came after the uprising, it may serve as "a probative connection" that justified "a global investigation of the acts performed before and after January 8, 2023 by the defendant."
In a note seen by AFP Friday, Bolsonaro's defense denied any involvement by the ex-president.
Bolsonaro "never had any relationship or participation in these movements," the note said, blaming the violence on "infiltrators."
Bolsonaro had for years sought to cast doubt on the reliability of Brazil's internationally praised election system, and had suggested he would not accept a defeat.
He never publicly acknowledged Lula's victory, and left for the United States -- where he remains -- two days before the inauguration.