Sitting less than a mile from the field in which Dudayev was killed by a Russian rocket, Zelimkhan Yandarbiyev showed little sign of being willing to compromise with the Kremlin, and called for a "popular uprising" in Chechnya and across the Caucasus.
Watched over by a frail-looking bodyguard, the 44-year-old Chechen - a poet and former bricklayer - launched into an attack on the "mafioso- like" Russia and accused President Boris Yeltsin of being responsible for the 16-month war.
"It is my firm purpose to bring peace to the Chechen people and, in the name of that peace, I will lead them in war," Mr Yandarbiyev said. "I will take the lead in a Jihad of the Chechen people in the name of Allah and their freedom."
The appointment of the little known Chechen has led to speculation that he may be a temporary leader, filling in until the separatist commanders settle the succession. But he gave no indication of planning to stand down soon.
In an oration paying tribute to the dead general, Mr Yandarbiyev praised his dignity, honesty and courage. "Someone had to lead from the front."
Mr Yandarbiyev, a vice-president during Dudayev's three years in power, can hardly be perceived as soft on Russia so soon after the death of the general who died in a Russian rocket attack while speaking on a satellite telephone in a field in southern Chechnya. He is less flamboyant than his predecessor - but he may prove equally difficult to negotiate with.
As the new Chechen commander-in-chief outlined his plan to journalists at his rebel hideout the citizens of Grozny were in a state of denial. They seemed as reluctant to believe in their leader's death as they are in President Yeltsin's promised, but never-delivered, ceasefire. There was no evidence of the three-day mourning period declared by the Chechen leadership.
In southern villages - the heartland of rebel support - groups of elders sat praying.
"I personally don't believe he is dead," said Nikolai Sambiyev, 44, one of the team of workers clearing up the rubble of the now demolished presidential palace.
"If a man dies, everyone gathers together. But there were only two or three, as if he were a dog."
Behind him three Soviet-era bulldozers ploughed through the tangled ruins of what was once Dudayev's seat of power. "He was the first President. If he was dead, they would have done more."
The general's death was confirmed on the rebel-run presidential TV channel on Tuesday by Shamil Basayev, a top Chechen commander. There have been many lies told in Chechnya, but Grozny's unwillingness to believe in Dudayev's death is partly rooted in a reluctance to concede any victory to the Russian troops who occupy their city.
At a make-shift market stall, Tymisha was convinced the general's death would make no difference. The war would carry on without him, she said.
So, evidently, will the opposition to Russia's presence in this remote republic.
"The soldiers provoke us all the time," she said. "They fire their guns in time with music they hear on their headphones just to inspire fear in us, so that we remain in a permanent state of shock."