"There will be no military solution to the question," both men told reporters, speaking in the wake of more than an hour of talks in the small town of Ordzhonikidzevskoye, part of the Ingushetia region which borders Chechnya.
"Of course there won't be war, for what reason would there be war?" Dudayev said.
Grachev said he and Dudayev, a former Soviet airforce general, spoke to one another as soldiers, not politicians. "Both being soldiers, we understood each other well," he said afterward, according to Itar-Tass.
Dudayev said the meeting concentrated only on military issues. "The question of independence is a political question, and the question of war or peace is a military one," he said. "We have agreed to decide peacefully the military issue, but a political decision has yet to be reached."
The Chechen leader said he was prepared to meet with President Boris Yeltsin to resolve political issues. "It may not be my wish, but it is necessary," he said.
Interfax earlier quoted Dudayev as saying the talks were the "last chance to avoid a war" with Moscow's forces in his region.
"The main result was a verbal announcement that there would not be a military solution. Both men were pleased with the talks," local administration chief Alekhan Pliyev said.
The meeting was the first between Dudayev and a top Russian official since the end of 1991, when he challenged Moscow by declaring his North Caucasus republic independent. Yeltsin has gone back on his initial plan to announce a state of emergency in Chechnya after serious fighting between Dudayev's forces and Moscow-backed rebels. But Russia is continuing a military build-up along Chechen borders.
Chechen Foreign Minister Shamsedin Yusef said the talks between Dudayev and Grachev were held on the initiative of Grachev, who earlier met the head of the Moscow-backed opposition Provisional Council which is trying to overthrow Dudayev.
Itar-Tass quoted Grachev as saying the two men had settled the problem of some 20 Russian servicemen captured during an abortive assault on the Chechen capital Grozny 10 days ago.
A nine-member delegation of lawmakers led by reformer Grigory Yavlinsky said Dudayev had agreed to allow the them to swap places with the imprisoned soldiers.
"I think the fact that we are here and we are going to stay here in Chechnya could stop possible intervention -- that is our main goal,'' Yavlinsky said in Grozny.
Yavlinsky slammed the Russian government's handling of the Chechen conflict, saying most Russians believe its actions have been "nonsense and very close to criminality."
He blamed "the former KGB, the military and Yeltsin himself."
Also Tuesday, Yeltsin urged the State Duma to issue an amnesty for people involved in armed conflicts in the North Caucasus region.
The Russian Journalists' Union accused the authorities in Moscow Tuesday of feeding unreliable information to the media about the crisis in Chechnya and of showing "scandalous disregard for the truth."
Two Russian prisoners released earlier by Chechnya returned to Moscow Tuesday, welcomed by Vladimir Zhirinovsky and a 10-piece orchestra of nationalist pensioners.
Zhirinovsky's Liberal Democratic Party brokered their release.
"Thank you, Vladimir Volfovich for freeing our Russian brothers," said pensioner Alexander Grigorev, who played the trumpet. (Reuters, AP)
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