Unions previously said the negotiations had reached a deadlock, after the government initially offered no increase.
The government is trying to contain its wage bill, which accounts for around a third of consolidated spending, to rein in a steep rise in debt that has been exacerbated by the Covid-19 pandemic.
"The offer is 1.5% which is pensionable and is on the baseline," Mchunu told a news conference. "Secondly, there is a cash gratuity which ranges from R1,220 to R1,695."
The unions had yet to respond to the offer. Mchunu said the government and unions would meet to discuss it on Tuesday.
Angered by the state's initial refusal to raise wages, one of the biggest public sector unions, the Public Servants Association (PSA), has balloted its members about a potential strike.
Other unions affiliated with the Cosatu federation that is closely aligned with the governing African National Congress have taken a more conciliatory approach, pursuing talks with the government in a bargaining chamber.
At the start of the negotiations in March, unions demanded a wage increase of inflation plus 4% in the 2021/22 fiscal year, as well as better housing payments and a risk allowance because of Covid-19.
Annual inflation was 5.2% in May.
Restraining rising wages is one of the key pillars of the National Treasury's fiscal consolidation strategy. Last year the government won a court case over wage increases that it refused to pay.
The PSA has challenged that ruling in a higher court.
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