Finance Minister Tito Mboweni has responded to suggestions he may resign with a tweet saying he was staying put in his post and working to fix South Africa's flagging economy.

"There is a malicious rumour that I have resigned. It is untrue," Mboweni posted on his Twitter account late on Sunday.

"I am firmly here as Minister of Finance. We have work to do. So much to do: fix our economy. No time for pettiness!"

The message came a week after President Cyril Ramaphosa strongly reprimanded him over a Twitter outburst following the sacking of Denny Kalyalya as head of the Bank of Zambia by President Edgar Lungu.

“Presidents in Africa must stop this nonsense of waking up in the morning and fire a Central Bank Governor! You cannot do that. This is not some fiefdoms of yours! Your personal property?! No!!" Mboweni messaged at the time.

“The President of Zambia must give us the reasons why he dismissed The Governor or else hell is on his way. I will mobilize!”

Following a complaint from Zambian authorities, Ramaphosa issued a statement in which he said the remarks did not reflect the views of the South African government.

"President Ramaphosa wishes to assure the government and people of the Republic of Zambia that the unfortunate remarks do not reflect the views of the South African Government and its people," his office said.

“The issue is being addressed to ensure that such an incident does not occur again."

Mboweni deleted the offending tweets. He subsequently tweeted dictionary definitions for the words "principle" and "humiliate".

A former governor of the South African Reserve Bank, the minister frequently stresses that the independence of the institution is sacrosanct.

Political foes of Ramaphosa are pushing for the mandate of the central bank to be revised. The issue was raised by former president Jacob Zuma in a letter to Ramaphosa ahead of a fractious meeting of the ruling African National Congress's national executive committee at the weekend.

Mboweni has in recent months openly disagreed with Cabinet colleagues on measures included in South Africa's response to the coronavirus pandemic, such as the contentious decision to ban alcohol and tobacco sales for several months.

He cautioned that the economy could not afford the resulting loss of tax revenue as it faces its biggest contraction in nearly a century.