South Africa's President Jacob Zuma has won the backing of the ruling ANC party, which rejected calls for him to resign over a controversial cabinet reshuffle.

The African National Congress on Wednesday acknowledged growing calls for Zuma to step down, admitting to "serious and difficult disagreement" over the president's sacking of respected finance minister Pravin Gordhan last week.

Zuma could either be ousted by the ANC recalling him, or a vote of no confidence in parliament that has been scheduled for April 18.

The party retains a large majority in parliament, and Zuma has easily survived previous confidence votes.

ANC secretary-general Gwede Mantashe told reporters on Wednesday that although the party had "reflected" on the resignation demands, "we won't recall President Jacob Zuma because opposition parties say so. It won't work that way".

Zuma has been under fire for several days - including from within his own camp - after dismissing Gordhan, a decision that caused the rand currency to plummet.

Gordhan's removal triggered unprecedented criticism from Deputy President Cyril Ramaphosa as well as the party's treasurer and several ANC allies.

Ramaphosa, who could succeed Zuma, described it as "totally unacceptable".

South Africa's powerful trade union federation Cosatu this week joined many anti-apartheid veterans, business leaders and civil action groups calling for Zuma to step down.

Mantashe - who was among those who had hit out at Zuma in recent days - said ANC would "close ranks" around the president and the party would iron out its differences with trade unions.

Mantashe blamed Gordhan's sacking on "the irretrievable breakdown" in relations with the president.

Gordhan was at loggerheads with Zuma for months, receiving support from several ministers and major foreign investors, as well as many ordinary South Africans.

Gordhan had campaigned for budget discipline and against corruption, but Zuma's allies accused him of thwarting the president's desire to enact radical policies to tackle racial inequality.

Gordhan's sacking contributed to a credit ratings downgrade to junk status on Monday by Standard & Poor's, further fuelling calls for Zuma to step down.

The president has defended his change at the Treasury, saying that the government's financial policies remained the same.