Mugabe addressed thousands of supporters outside the headquarters of the ruling ZANU-PF party, issuing a clear threat to Evan Mawarire, the pastor who has become the figurehead of a new opposition movement.
"The Mawarires. I want to warn them very strongly," Mugabe said in a fiery 45-minute speech.
"ZANU-PF will not tolerate any nonsense.
"Once you begin to interfere with our politics, you are courting real trouble.
"We know how to deal with our enemies who have been trying to bring about regime change."
Mugabe, who took power in 1980 and is now aged 92, has often used his security forces to crack down ruthlessly on any sign of dissent in Zimbabwe.
But a wave of street demonstrations and strikes has shaken his government, which has run out of money and is struggling to pay its soldiers and civil servants.
In the latest sign of growing national instability, veterans of Zimbabwe's 1970s independence war, who have previously been loyal supporters of the president, issued a statement last week denouncing him.
"When we find out who the people were, the party will discipline them. The punishment will be severe," Mugabe said in his first comments on the veterans' criticisms.
Douglas Mahiya, a spokesman for the war veterans who issued the communique, was Wednesday summoned for interrogation by the police, his lawyer said.
"They said they want him for questioning," lawyer Charles Nyika told AFP a few hours after Mugabe's warning.
Earlier this month, many offices, shops and some government departments closed for a one-day nationwide strike to protest over the country's economic collapse -- worsened by a severe drought.
Mugabe on Wednesday also repeated his accusations that western countries were fuelling opposition against him.
"The foreign embassies in the country that are interfering with our politics... I want to warn them to desist from it," he said.
"(They) try and subvert our system of government."
Mugabe's audience on Wednesday was made up of party loyalists, some of them waving the party flag and wearing party regalia displaying his portrait.
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"There is one centre of power and that is Comrade President Mugabe. (He) should rule until death," Dickson Mafios, a provincial party chairman, told the crowd.
Mugabe, who is increasingly fragile, has vowed to stand for re-election in 2018, though party seniors have long been jockeying to step into the role when he dies.
"As long as the party still wants me to serve and if I still have the energy and still have the life and the blessings of God, I will continue," he said.
Mugabe's wife Grace and vice-president Emmerson Mnangagwa are among the possible successors of the world's oldest president.
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