Zimbabwean President Robert Mugabe used his Independence Day speech to promise tough action against his opponents.
A demonstration near Johannesburg called for Mr Mugabe's removal
He also reiterated plans for greater state control over the mining industry.
Zimbabwe on Tuesday marked 26 years since independence from Britain, amid a deepening economic crisis with inflation at 900% per annum.
Mr Mugabe called on Zimbabweans to stand together and blamed the current problems on a persistent droughts and "evil" sanctions by Western nations.
In an apparent warning to opposition leader Morgan Tsvangirai, who has called for mass action against the government, Mr Mugabe said those who plotted against him were playing with fire.
"Anyone... who dares lead any group of persons to embark on a campaign of violence or terrorist activities will be inviting the full wrath of the law to descend mercilessly on him or on those who follow him," he said.
Mr Mugabe said the government would press ahead with plans to extend greater state control over the mining industry.
"Non-renewable resources are ours in the first place, Mugabe said.
"You, the investor, will get a reward, yes, but that reward will be balanced by what we keep for ourselves."
In South Africa, a few dozen of the many thousand Zimbabwean exiles who live in the country demonstrated near the African parliament, in Midrand, north of Johannesburg, calling on Mr Mugabe to resign so they could return home.