His replacement, Zelimkhan Yandarbiyev, 45, who is seen in Moscow as a hardliner, took over the rebel leadership with a vow that the fight for independence from Russia would go on, according to Itar-Tass.
Although there is speculation that Mr Yandarbiyev, a literary scholar who helped muzzle the media in Chechnya after Dudayev declared independence in 1991, will not last long, there were other ominous signs he conflict will drag on.
Mr Yeltsin has refrained from sounding triumphant about the death of his so-called arch-enemy, whom he called a "bandit". Mindful he has yet to fulfil his promise to end the Chechen conflict before the Russian presidential election in June, he said: "With or without Dudayev, we will end everything in peace in Chechnya."
Confirmation of the death of the 52-year-old former Soviet air force general came with an announcement on Chechnya's rebel-run "Presidential TV" by a top commander, Shamil Basayev. In a move that will anger Moscow, Turkey's President, Suleyman Demirel, said he was saddened by the news.
Among front-runners eventually to replace the general is Mr Basayev himself, a celebrated fighter whose features appear on posters across southern Chechnya. Russia would prefer Aslan Mashkhadov, Chechen chief of staff, who took part in last summer's failed peace negotiations and who is viewed as a moderate.
Dudayev reportedly died after being hit by a Russian rocket attack near the village of Gekhi-Chu, an area of south-west Chechnya the Russian military continues to bomb, despite Mr Yeltsin's insistence that all major operations ended with his 31 March declaration of a ceasefire. However, specific attacks on rebel fighters came into the category of "special operations".
The Russians managed to track Dudayev from the emissions of the satellite telephone he was using and use them to target the rockets which killed him, according to British intelligence sources . The Russian military performance in Chechnya over the last 18 months has been woefully short of expectations. But the Russians, who have long believed that the person who controls the electromagnetic spectrum will win the next war, finally succeeded in using their technological expertise to score a precise hit which was more significant than the employment of tens of thousands of Russian troops in the blundering Chechen campaign.
According to intelligence sources, the Russians would have known the number that Dudayev was calling and the frequency. From there, it would not have been difficult to home in on the satellite telephone transmitter and direct multiple rocket launchers to hit the target.
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