The men had given President Thabo Mbeki's office 24 hours from Monday to respond to a request to either seek their extradition to South Africa or ensure they were not tried in Equatorial Guinea.
"We did not hear from the president's office so we are proceeding with a court application," lawyer Alwyn Griebenow told Sapa.
"The application will probably be heard next Tuesday in the Pretoria High Court," he said.
The alleged mercenaries were arrested at Harare International Airport two months ago when they apparently landed to refuel and pick up military equipment. They were all travelling on South African passports.
The men are being held in a Harare jail.
Zimbabwean authorities claim they were on their way to join 15 suspected mercenaries - including eight South Africans - arrested in Equatorial Guinea around the same time.
The men are accused of planning to overthrow Equatorial Guinea's leader Teodoro Obiang Nguema.
Zimbabwe President Robert Mugabe earlier this month held talks with Obiang after which an official told French news agency AFP that Mugabe had agreed to hand over the men for trial and a possible death sentence in Equatorial Guinea.
However, there has not been any official statement from the Zimbabwean government about extradition of the 70 men.
Mbeki's spokesman Bheki Khumalo said the court papers were served on the government in the morning.
"The State attorneys have been instructed by the government to file a notice to oppose the application."
He declined to discuss the merits of the matter. - Sapa
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