He appeared to rule out independence for the Chechens, however, when he said that they would have representatives in the Russian parliament.
Mr Yeltsin made his television broadcast from the sanatorium outside Moscow where he is recovering from a heart attack.
Dressed in a grey suit, he read in a wooden voice from a prepared text. But his appearance was a public relations triumph compared with his performance in December when, as the army was entering Chechnya, he used a nose operation as an excuse to stay out of the public eye and issued only curt statements.
The Kremlin leader, who may stand for re-election next year despite poor health, came as near as he could to apologising for his military adventure in the Caucasus.
"It is bitter to realise that the price which had to be paid for the implementation [of decrees ordering the intervention] was very high," he said.
"I bow my head before the memory of those who sacrificed their lives, defending the basic values without which the existence of any state is unthinkable."
Sending troops to Chechnya had been unavoidable, as all other means of ending the rebellion had been exhausted. It had also been legal, as the Constitutional Court ruled earlier this week, he said.
Mr Yeltsin said talks to end the conflict had been "crowned with success". A "real opportunity" had emerged to restore peace, and hawks on both sides must be "curbed". Explaining the accord signed by Russian and Chechen negotiators on Sunday, he said the disarmament of Chechen gunmen would "become the basis for the pull-out of Russian troops who have fulfilled their duties".
Evidently, he envisaged the guerrillas giving up their guns before the Russians withdrew, a timetable with which the Chechens might disagree.
Two brigades of Russian troops would be permanently stationed in the area, he said. He promised he would choose an "experienced and knowing man" as his representative in Chechnya to monitor human rights. "World experience shows that practically any issue can be settled by means of talks, relying on the law and goodwill."
The President promised to rebuild Chechnya and called on people in the region to show goodwill. This may cut little ice with the Chechens, once they grasp that Mr Yeltsin has ruled out independence. There would be free elections, Mr Yeltsin promised. The Chechen people should have "their own legitimate bodies of power". But then he added the poisoned words: "Representatives of Chechnya, as well as other Russian territories, should be included both in the Federation Council [the upper house of the Russian parliament] and the State Duma [the lower chamber]."
It remains to be seen whether Mr Yeltsin's explanation will restore his popularity. But it was announced that a public committee had been formed to gather signatures in support of Mr Yeltsin's candidacy in the presidential elections next June.