Kaczynski's coffin was carried off the plane by soldiers and blessed by priests. It was taken in a procession the streets to the presidential palace, where the body will lie in state for several days.
The bodies of the other victims have been taken to Moscow, where relatives have gathered to begin the task of indentifying the remains.
Earlier thousands of Poles gathered at the presidential palace in Warsaw to pay their respects as sirens and church bells rang out at noon in tribute.
Others flocked to churches across the nation to lay flowers, light candles, sing hymns and pray.
A week of national mourning has been declared in Poland following the disaster.
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.
Lech Kaczynski's wife, Polish church leaders and families of Katyn massacre victims were also killed.
A significant part of Poland's political establishment was wiped out as all passengers on board the aircraft, including senior government officials and parliamentarians, perished.
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.
Tusk described the accident as "the most tragic event of the country's post-war history", before flying to the crash site later on Saturday where he and Putin, met and laid flowers together.
Shock and grief
Al Jazeera's Jonah Hull, reporting from central Warsaw, said there was a sombre atmosphere on the streets.
"It is really striking that so many people are gathering here, tens of thousands of them, and there is hardly a sound.
"They are hardly talking to each other. Many people have held a vigil through the night and many of them are visibly overcome by shock and grief."
Poland declared a week of national mourning following the president's death
Following the constitution, Komorowski, the speaker, took over as interim head of state until a presidential election is held.
Al Jazeera's Alan Fisher, reporting from Warsaw, explained the process.
"There has to be an election within 60 days, and the date has to be announced within two weeks.
"People are looking to the presidential election before Poland will really get back on the rails."
Komorowski said he would announce the date of the poll after talks with all political parties. Poland had been due to hold a presidential election in October, when Lech Kaczynski, a conservative, was expected to run against Komorowski, a liberal.
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.
"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.