The strike comes in the wake of days of violent protests over a lack of basic services and jobs in which police and demonstrators have repeatedly clashed.
As the strikers marched through Johannesburg, hundreds of passengers were stranded in the city's central business district.
"We want the employers' organisations and the government to come to the table and negotiate on a bonafide position"
Simon Riekert, Independent Municipal and Allied Trade Union
Bus services ground to a halt and licensing stations remained closed.
Haru Mutasa, Al Jazeera's correspondent in Johannesburg, said: "A couple of thousand people marched to the mayor's office where they attempted to enter the building.
"They were prevented from entering by police. They presented their demands to officials and said they would return on Tuesday."
Mutasa said Zuma had promised 500,000 jobs by the end of this year and people "are waiting to see where those jobs will come from".
"The country is in a recession, people are being retrenched, more people are frustrated," she said.
"The fear is that if municipal workers do not go back to work ... people in the townships, the ones who are most angry, will take to the streets again.
"If that does happen, there could be more violence in the coming weeks."
Simon Riekert, a spokesman for the Independent Municipal and Allied Trade Union, one of the organisations involved in the strike, told Al Jazeera: "We are in a position to be amicable as far as any agreement is concerned.
"However, we want the employers' organisations and the government to come to the table and negotiate on a bonafide position."
The unions want a 15 per cent salary increase to cushion their members as the country grapples with its first economic recession in 17 years.
Employers increased their offer to from 11.5 per cent to 13 per cent on Monday, but this was rejected.
The strikes are the latest sign of discord between the ruling ANC government and its labour union allies which helped Zuma win an April election with promises to improve the lives of millions of South Africa's poor.