The heads of Poland's armed forces, the central bank governor, deputy ministers and 15 MPs were among those killed when the jet tried to land in heavy fog and crashed in a forest.
Wreckage, including the engines, was scattered across a forest and parts of it burned for more than an hour.
The officials had been on their way to the city of Smolensk to take part in reconciliatory ceremonies commemorating the 70th anniversary of the Katyn massacre where Russian forces killed more than 20,000 Polish prisoners of war.
Kaczynski's wife, Polish church leaders and families of Katyn massacre victims were also killed.
Al Jazeera's Jonah Hull, reporting from Warsaw, said: "Katyn was a major blight between the Soviet Union and Poland for many many years ... Thousands of prisoners of war massacred, among them senior officers, troops and also intellectuals - the elite really, who were wiped out effectively in that massacre.
"The irony, of course, is not lost on many people that in Saturday's tragic crash, the elite were all on board one aircraft going towards Katyn to commemorate that event."
Following the constitution, Bronislaw Komorowski, the speaker of the lower house of parliament, took over as interim head of state and a presidential election has to be held before the end of June.
Komorowski said he would announce the date of the poll after talks with all political parties.
Dmitry Medvedev, the Russian president, has appointed Putin to chair a special commission to investigate the crash.
Alexander Alyoshin, the first deputy chief of the Russian air force's general staff, said the plane's pilot repeatedly ignored instructions from air traffic controllers.
"The head of the air traffic control group gave a command to the crew to put the aircraft into the horizontal position and when the crew did not implement this order, several times gave orders to divert to an alternative airport," he was quoted as saying by Interfax news agency.
|Officials said the aircraft crashed through
the trees and broke into pieces [EPA]
"Despite this, the crew continued the descent. Unfortunately this ended in tragedy."
Authorities have found both flight recorders, commonly known as "black boxes", from the jet.
Komorowski, Poland's acting president, declared a week of mourning after the crash.
"We are united - there is no [political] left or right - we are united in national mourning," he said.
Poland had been due to hold a presidential election in October, when Kaczynski was likely to have run against the liberal Komorowski.
The conservative Kaczynski, who had served as president of Poland since 2005, had a reputation for being incorruptible and was a popular figure.
Marek Matraszek, a political consultant in Warsaw, told Al Jazeera that politically, Kaczynski had been losing in popularity recently.
"But even his deepest enemies would not deny that he was hugely respected by the Polish people," he said.
"Many of his political opponents, while disagreeing with him politically, respected him for his career, his personality, his principles ... This will very much go forward into cementing how Poles will remember him: not as a politician but rather as a man of deep principle."
Matraszek said the loss of so many politicians would have a significant effect on the political scene in Poland.
"This is an issue that cuts across political barriers ... Every political party and every part of the political establishment has been affected. These were very senior people with a great deal of experience who will be very difficult to replace ... Many of the people who died had no real successors."