At an Independence Day rally last week the far-right leader fired off a warning at the Supreme Court, which has ordered an investigation of him, saying it would "suffer the consequences" unless it backed off.
He also renewed his attack on the country's electronic voting system ahead of elections in 2022.
"President Jair Bolsonaro is threatening democratic rule in Brazil," the rights body said in a statement released on September 15, which is observed as the International Day of Democracy.
"He is pursuing campaigns to intimidate the Supreme Court, signalling that he may attempt to cancel the 2022 election or otherwise deny Brazilians the right to elect their leaders, and violating critics' freedom of expression."
Bolsonaro's recent speeches were part of a "pattern of actions and statements that appear designed to undermine fundamental rights, democratic institutions, and the rule of law in Brazil," HRW added.
Two days after his vehement criticism of Brazil's federal institutions in front of thousands of supporters in Sao Paulo, the president sought to back off, insisting his jabs had been made "in the heat of the moment."
Yet, "he did not backtrack from his unproven claim that Brazil's electoral system is unreliable," HRW pointed out.
Bolsonaro, whose popularity is at an all-time low, is seeking to fire up his base in the face of a flagging economy, soaring unemployment and inflation, and a series of investigations targeting him and his inner circle.
The president is also under fire for his handling of the coronavirus outbreak, which has claimed more than 587,000 lives in Brazil.
Bolsonaro, who backed Donald Trump's claim of fraud in last year's US presidential election, warned in January that the chaos that rocked Washington as Trump refused to concede could repeat in Brazil or "even worse," as he sought once again to cast doubt on Brazil's voting system.