Defense Minister Igor Sergeyev and navy chief Vladimir Kuroyedov submitted their resignations over the loss of the Kursk, one of Russia's most advanced submarines, but Putin said he would not accept them.
Seeking scapegoats, he said, would be "the most mistaken response." He said he would not punish people without reason, and called for unity.
"I take a full sense of responsibility and sense of blame for this tragedy," he said in an interview with Russia's RTR television as the country held a day of mourning for the dead, with flags lowered across Russia and church services.
"Nothing will be done, I repeat, until a full understanding has been gained about what happened and why," Putin said. "(We need to find out) if there are guilty, truly guilty people, or it was simply a confluence of tragic circumstances."
In a country where authoritarianism runs deep, Putin's comments displayed a remarkable humility, sensitivity and eagerness to regain the nation's confidence, all unprecedented for a Russian leader.
Russians have assailed Putin and his government for their slow, contradictory reaction to the disaster and the botched rescue operation, and many observers expected Putin to respond by firing top military brass.
Putin disagreed. Immediately firing people would merely be repeating the mistakes of past regimes, he said.
Some family members aimed their outrage at Putin.
"I didn't go to meet Putin. I cannot see that person," Marina Stankyevich, wife of one of the crew's doctors, told NTV commercial television. Several parents refused to participate in memorials.
"Until the bodies of our husbands are retrieved, until we see them with our own eyes, we will not mourn," said Oksana Dudko, whose husband Sergei was the ship's deputy commander.
Vyacheslav Shchavinsky, the father of one of those killed, said it was terrible to think about what it must be like aboard a downed submarine.
Russian officials now think the submarine's crew died almost instantly when an explosion ripped through it. Earlier they said they thought they heard tapping from inside the ship's hull.
"You know the way it happens, they couldn't understand that one minute they were carrying out a military exercise the next, there was a blast," Shchavinsky said, holding his son's prized guitar.
Divers who tried to rescue the sailors said it was impossible to immediately tell what caused the explosions.
"We tried to hammer code on the hull when we got there, and there was no response," Julian Thomson, spokesman for the diving company Stolt Offshore, said on behalf of the divers. Then we opened the hatch, and found the submarine full of water. What happened before that, we don't know."
The divers expected trouble, but it proved a technically simple, if emotionally demanding, task to descend 350 feet under the Barents Sea to open the submarine's emergency hatch and find it completely flooded.
A Russian rescue bell tried unsuccessfully for a week to reach the Kursk after it went down on Aug. 12.
Russian efforts were defended by one Kursk parent First Class Captain Vladimir Geletin, who led Russian rescue efforts. His 25-year-old son, Boris, was a lieutenant on board.
"We did everything we could, everything we could. Yes, the fleet does need good emergency rescue units and we didn't have them," Geletin said.
Geletin lashed out at critical media coverage of the navy's rescue effort. The navy has come under fire for making contradictory and unreliable statements about the crisis.
"The fleet command always told the truth. ... (At the beginning) nobody could say exactly what had happened to the vessel," he said, explaining why initial navy reports played down the seriousness of the Kursk's situation.
"Nobody could have said right the vessel is on the sea bed, that means everybody is dead," he said.
Putin also lashed out at critics of Russia's rescue efforts and his own actions, pointing the finger at the so-called "oligarchs" influential and hugely wealthy businessmen whom Putin has set out to challenge for depriving state coffers of funds.
"And those who are in the first row of the sailors' defenders, they have turned out to be those people who in their time prompted the breakdown of the army, navy and the state," he said.
"They should have sold their villas in France and Spain," he added.
The botched rescue highlights the crumbling state of Russia's impoverished military, Putin and Geletin said.
"You all know the reason very well: The fleet has many problems, like the whole military, like the whole country," Geletin said.
The Kremlin promised compensation to the families, who had relied on the sailors' meager salaries for subsistence. The federal government promised a one-time payment equal of an average of $7,000 per family equal to 10 years of pay for a submarine officer, said Deputy Prime Minister Valentina Matviyenko.
Putin, meanwhile, promised to restore the honor of the beleaguered military and the nation.
"It grieves me, the theory lately that together with the Kursk, the honor of the navy also drowned, the honor of Russia," he said. "Our country has survived a lot."
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