"The air traffic control officer gave several orders to divert but the plane continued with its descent," said Alexander Aleshin, a top Russian Air Force official. "Unfortunately, this ended in tragedy."
Russian President Dmitry Medvedev appointed Putin to head an inquiry commission and sent Emergency Situations Minister Sergei Shoigu to the scene of the crash, the Kremlin said.
"We had a lot in common as presidents and as ordinary people and I can assure you that the death of Lech Kaczynski will be investigated and that we will uncover all the circumstances of this plane crash," Medvedev said Saturday.
Other Polish officials killed in the crash include Aleksander Szczyglo, the head of the National Security Office; Jerzy Szmajdzinski, the deputy parliament speaker; Andrzej Kremer, the deputy foreign minister; and Gen. Franciszek Gagor, the army chief of staff, according to Kaczynski's Law and Justice Party.
The party also said that Slawomir Skrzypek, head of the National Bank of Poland, was killed.
"The entire top military brass, including the chief of defense and all the services, were on the plane," Valasek said. "You're looking at a situation, in effect, of the decapitation of the military services."
Putin spoke Saturday at the crash site, where charred pieces of the airplane were strewn through a wooded area. Some pieces, including one of the wheel wells, were upside down.
"As our first priority, we must establish the causes of this tragedy," he said. "As a second priority, we must do everything in our power to assist the families and relatives of the deceased."
The plane carrying Kaczynski was refurbished and repaired last year, according to Alexei Gusev, general director of Aviakor Factory, the company that performed the service.
"Speaking openly, we believe that this tragedy could not have been caused by equipment failure," he said.
Kaczynski had been president since December 2005, after he defeated rival Tusk in the second round of voting.
There is going to be a huge gap in public life in Poland. The most important people are dead.
--Magdalena Hendrysiak, Warsaw resident
The two men did not have a good relationship. In parliamentary elections in 2007, Tusk's Civic Platform beat the Law and Justice Party of Kaczynski's twin brother, Jaroslaw Kaczynski, who was prime minister at the time.
Tusk put political differences aside as he spoke to the nation Saturday.
"I wanted, in the name of all the Polish people, to pass words of condolences to the familiy of the Polish president, to his daughter, to his mother, to his brother, and to all the families of all the victims," he said.
Tusk and Polish Cabinet ministers held a special meeting Saturday morning to discuss the situation.
Elections must now be held within 60 days, said Dariusz Rosati, Poland's former foreign minister.
Valasek pointed out, however, that the Polish president is the head of state, not head of government -- meaning essential services will continue.
"The role of the Polish president is not quite ceremonial ... he has some very real powers, but at the end of the day, the day-to-day running of the government is in the hands of the prime minister and the (cabinet) ministers," Valasek said. "Continuity is assured in ways that would not necessarily be assured in the case of the death of the U.S. president."
Meanwhile Saturday, condolences poured in from around the world, including from British Prime Minister Gordon Brown, German Chancellor Angela Merkel, and Britain's Queen Elizabeth and Prince Charles.
"President Kaczynski was a distinguished statesman who played a key role in the Solidarity movement, and he was widely admired in the United States as a leader dedicated to advancing freedom and human dignity," U.S. President Barack Obama said in a statement.