Two groups of strikers in Durban defied the order, with workers blocking an entrance at King Edward Hospital and police firing rubber bullets to clear the entrance to Addington Hospital, according to the Sapa news agency.
RFI correspondent Jean Jacques Cornish, speaking from Johannesburg,
said that there had been limited improvements in relations between strikers and the state.
“The improvement is not of a nature that we could say things are normalised,” he said.
“We are still dealing with acts of intimidation, though they are isolated now."
Police at Johannesburg hospitals were guarding entrances during peaceful protests, while in Cape Town health officials said only a handful of hospital workers were off the job.
The defence ministry said military teams were called in to aid doctors and replace striking support staff in cleaning bed linen and providing meals at 37 hospitals.
Bruce MacGregor, from the South African labour law firm Macgregor Erasmus, told RFI that public sympathy for the strikers is not guaranteed.
"There is a great deal of sympathy for the strikers, but that sympathy is being eroded by the behaviour of some of them, [including] intimitdating non-striking workers, blocking hospitals, preventing patients from getting treatment," he said.
Unions are demanding an 8.6-percent wage increase and a 1,000-rand (108-euro) housing allowance. The government has moved to unilaterally implement a seven percent raise and a 700-rand housing allowance.
"Government appeals to the public sector unions to sign the offer without delay and further appeals to all public servants who are on strike to return to their posts," the cabinet said in a statement Monday.
Inflation is running at 4.2 percent in South Africa, but unions argue that big increases are needed to close the gap between rich and poor, in one of the world's least equal societies.
Unions are politically powerful and a key ally of President Jacob Zuma's ruling African National Congress, but tensions have erupted over both wages and general economic policy.
The country's largest teachers' union said it planned to contest the court ordering "essential services" employees back to work, saying it was overly broad.
"We have resolved that we are not going to retreat from continuing with our demonstrations until our demands are met," the South African Democratic Teachers' Union said in a statement.
"Our strike is legal and we will continue to intensify our actions."