His appointment last week, after the sacking of the internationally respected Pravin Gordhan by President Jacob Zuma, has seen the currency plunge and threatens to split the ruling African National Congress.
The main opposition party has called for a no-confidence vote against Zuma.
The country faces the risk of being downgraded to junk status due to weak growth and the political upheavals after it got a reprieve last year.
South Africa’s economic growth slowed to 0.3 percent in 2016 from 1.3 percent in the previous year.
“As government, our focus is now very much on the radical transformation of our economy so that all who live in South Africa can benefit from the economy. Tough and unpopular choices will have to be made to ensure such a vision,” Gigaba told a media briefing, without elaborating.
The rand extended its losses against the dollar on Monday, hitting a session low of 13.6900 per dollar earlier in the day before trimming some of the losses to trade at 13.4900/dollar by 1527, 0.5 percent weaker, as the market factored in the strong resistance to Zuma. Government bonds also weakened.
In his maiden media briefing on Saturday, Gigaba also signalled he would oversee the redistribution of wealth to the black majority, as favoured by Zuma. Some members of the ANC had criticised Gordhan for not taking adequate steps to do so.
The ANC has been criticised by its supporters over inequality in a country where black people make up about 80 percent of the population of 54 million, but ownership of land and companies remains mostly in the hands of white people, who account for about 8 percent of the population.
Gigaba was yet to spell out how he plans to radically transform the economy, while maintaining the fiscal discipline the Treasury was known for.
He promised to stick with fiscal plans set out in February’s budget presented by Gordhan, including plans to seek up to $2 billion per year in foreign funding in the next three years.
Some analysts feared that budget discipline will falter despite the risk that the country’s credit rating will be downgraded to “junk” status.
On Friday, Moody’s will review its Baa2 rating, which is two notches above sub investment grade, followed by S&P Global Ratings – at one rung from junk – at the beginning of June.
Fitch, also one notch above junk, is not bound by a timeline.
A downgrade to junk would increase South Africa’s debt-servicing costs, seen at 144 billion rand ($11 billion) in the 2016/17 fiscal year.
Paying higher debt costs would mean less money for critical services such as housing and sanitation, which could incite more protests that have rocked townships across the country and eroded support for the ruling ANC which had dominated politics since the end of white-minority rule in 1994.
Previously home affairs minister, Gigaba said he was an “experienced politician” and well-educated, adding that nobody should doubt his ability to adapt to the new portfolio.
“The assurance we can give is … we are not a bunch of wild gunmen running amok, gung-ho into Treasury, to do different things. We are going maintain the programmes that are being implemented,” Gigaba said.
“We indicated to the ratings agencies that there will be no change in our fiscal stance. We are the same government.”