The former Soviet president, Mr Mikhail Gorbachev, joined a nationwide chorus of disapproval yesterday when he criticised Mr Putin's "serious mistake" in not hurrying to the Kursk disaster scene.
"Speaking as a decision-maker and somebody who understands these things, I think that either he was misled or he misjudged the situation," Mr Gorbachev said in an interview with Moscow's Echo Radio.
He added that Mr Putin "should have gone to the scene to take charge of the rescue operation and to decide on the participation or otherwise of our partners in the world community".
Mr Gorbachev said the Russian president had "let the moment pass" when it might have still been possible to save the crew of the stricken nuclear submarine, whose chances of survival look increasingly grim.
Mr Putin yesterday responded to criticism that he had not cut short his summer holiday in the wake of the disaster in the Barents Sea by saying he had not wanted to "interfere" with the rescue effort.
He told Interfax in Yalta, Ukraine, that his "first wish" had been to fly straight to the Barents Sea. "But I changed my mind, and I think I did the right thing," he said, because "the arrival of non-specialists and high-ranking officials on the scene of a disaster does not help, and very often it gets in the way."
"Everybody should keep to their proper place," he said.
But the Russian press has criticised Mr Putin for not returning from the Black Sea resort town of Sochi to personally take charge of the crisis, while the liberal lawmaker Mr Boris Nemtsov, a supporter of Mr Putin in the State Duma, denounced the president's behaviour as "amoral".
"As the supreme commander-in-chief, he has no right to vacation while his subordinates, Northern Fleet sailors, face this drama," Interfax quoted Mr Nemtsov as saying yesterday.
Others said Mr Putin, a former KGB spy, was insensitive to human suffering.
By not immediately accepting Western aid to save the crippled nuclear submarine, Mr Putin had "deliberately sacrificed the crew", Ms Valentina Melnikova, head of the Soldiers' Mothers Committee, charged in an interview published yesterday in the French daily Aujourd'hui/Le Parisien.
But Mr Putin denied he had turned down Western offers of help in the rescue mission out of misplaced pride.
"As for our foreign colleagues' participation in the rescue operation, I must say that the Russian side never reject this," he said.
"Bad weather was the main obstacle up to now," he said. "That is why the presence at the scene of the tragedy - besides Russian rescuers - of rescuers from other governments and of other nationalities, unfortunately would not have changed the weather for the better."
Mr Putin had said on Wednesday the situation aboard Kursk was "critical", but stressed that Russian rescue workers were well equipped to lead the operation on their own. The Russian foreign ministry appealed for British and Norwegian help only hours later.