Zuma's sacking of Finance Minister Pravin Gordhan in last Thursday's reshuffle has outraged allies and opponents alike.
More than 60,000 people marched in South African cities on Friday in largely peaceful protests to demand President Jacob Zuma quit after a cabinet reshuffle triggered the latest crisis of his presidency.
His decision to sack the finance minister Pravin Gordhan has led to rating downgrades and public anger.
Fitch on Friday followed S&P; Global Ratings and downgraded South Africa to "junk", citing Gordhan's dismissal as one reason.
S&P; had issued its downgrade on South Africa in an unscheduled review on Monday.
Despite the criticism, the president's power seems firmly in place.
TRT World's Lynsey Chutel reports from Johannesburg.