The far-right president and top generals have repeatedly evoked the threat of a "coup" in recent days -- not against Bolsonaro, but against Congress and the Supreme Court, which are locked in an increasingly bitter battle with the executive branch.

Though analysts say any military intervention in Latin America's biggest democracy is unlikely for now, constant talk about it has some in Brazil worried about how Bolsonaro could react under growing pressure from the coronavirus crisis, the painful recession it is expected to trigger, rising disapproval ratings and a series of uncomfortable investigations and impeachment attempts.

Bolsonaro, a former army captain who openly admires Brazil's 1964-1985 military dictatorship, has cultivated a special relationship with the military, a year and a half into his term.

Ten of his 23 cabinet ministers are military officers, and 3,000 more have high-level jobs in his administration.

"We, the members of the armed forces, are the ones truly responsible for democracy in this country," Bolsonaro said Monday.

Evoking the threat of an institutional "coup" -- a word used often in Brazilian politics these days -- he denied the military would ever follow orders to intervene against Congress or the courts.

"We would never follow absurd orders," he told Band TV.

"But," he added in the same breath, "we also won't accept a politicized trial to destroy a democratically elected president."

- No tanks in streets -

With the institutional battle escalating, Bolsonaro recently claimed the Constitution gave him the right to use a military intervention to "restore order" in Brazil.

However, legal experts insisted that did not include using the army against another branch of government.

Bolsonaro is facing some 30 impeachment petitions in Congress and an opposition push to annul his 2018 election over alleged dirty dealings by his campaign.

His inner circle is also being targeted in a series of investigations, including one into allegations his son Carlos oversaw a disinformation campaign to benefit his father.

Last weekend, Bolsonaro supporters shot fireworks at the Supreme Court building and threatened to tear the justices' robes to rags.

Bolsonaro's Education Minster Abraham Weintraub meanwhile called the justices "idiots" and said they should be thrown in jail.

Last week, his secretary of government, active-duty General Luiz Eduardo Ramos, called it "outrageous" to imply the military would act against democracy.

But in an ominous warning to what he called the "other side," he added: "Don't push it."

Bolsonaro's powerful national security minister, reserve general Augusto Heleno, has for his part warned Brazil's "national stability" would be at risk if investigators tried to seize the president's cell phone in an ongoing obstruction of justice probe, as opposition parties have requested.

However, an actual military intervention in Brazil is "absolutely not" looming, said Nelson During, chief editor at security and defense news site Defesanet.

"A democratic rupture remains extremely unlikely in Brazil," said the Eurasia Group consultancy.

"We would put the odds of a democratic breakdown, defined by the closure of Congress or the courts, to be under five percent."

- 'Unpredictable reactions' -

But constantly raising and then denying the possibility of a military intervention is part of a "strategy of threats directed at the Supreme Court to fend off what are seen as affronts to the executive," said Maud Chirio, a historian at Gustave Eiffel University in Paris.

And although the military is keen to protect its image -- dirtied by two decades of rights abuses during the dictatorship -- "military leaders are showing their absolute solidarity with Bolsonaro, for now," she told AFP.

Eventually, "some form of coup d'etat is possible if the other branches of government... decide to play the impeachment card or hamstring Bolsonaro with countless investigations against him and his family."

But "a classic coup, with tanks outside the seat of government in Brasilia," is highly unlikely, said Carlos Fico, a professor of military studies at the Federal University of Rio de Janeiro.

"The military would have a hard time acting against (democratic) institutions," he said.

But hardcore Bolsonaro supporters could follow through on their threats to try to shut down Congress or the Supreme Court.

With just 30 percent of voters now supporting the president, that could lead to unrest and "unpredictable reactions from the military police," which strongly backs the president, he added.