RIO DE JANEIRO — President Jair Bolsonaro of Brazil was struggling to govern effectively long before the explosive resignation speech of his star cabinet minister, who basically called his soon-to-be former boss a criminal.

Mr. Bolsonaro became a president without a political party in November, after falling out with leaders of the Social Liberal Party, which had backed his presidential bid.

Several political allies — including two of Mr. Bolsonaro’s sons — are under investigation in a series of criminal and legislative inquiries. They include suspected money-laundering schemes and defamatory disinformation campaigns waged online.

In recent weeks, Mr. Bolsonaro’s strikingly dismissive response to the coronavirus pandemic, which he has called a “measly cold” that cannot be allowed to throttle economic growth, generated calls for impeachment at home and bewilderment abroad.