Investigators were trying to determine the cause of the crash, which occurred as the delegation was heading from Poland to mark the 70th anniversary of the Soviet execution of more than 20,000 Polish officers at Katyn, Russia.
The 26-year-old Russian-made jet went down in heavy fog a half-mile from the runway of the Smolensk airport in western Russia Saturday, killing all 96 people aboard, including the president's wife, Maria.
In Warsaw, a hearse bearing Kaczynski's body passed mourners lining streets as it headed to the Presidential Palace, The New York Times reported.
After the plane carrying her father's body landed in Warsaw, his daughter, Marta, kneeled at his coffin and rested her forehead on it before other relatives paid their respects.
Senior Polish officials offered assurances the government would continue to function normally after the loss of Kaczynski, many top staff members, more than a dozen members of Parliament and military leaders. New acting military chiefs had been in place Saturday and a new interim central bank chief was named Sunday, the Times said.
Meanwhile, the newspaper said, Russian and Polish investigators began analyzing evidence from the plane's flight recorders.
Prosecutors, forensic pathologists and crash investigators were working with their Russian counterparts in Smolensk and Moscow, Polish and Russian officials said.
Russian officials said air traffic controllers at the Smolensk airport had ordered the crew of the presidential plane not to land there because of the bad weather and warned the plane was below the glide path before recommending it go to another airport, the Times said.
Aleksandr Bastrykin, chief of the prosecutor general's investigation committee in Russia, told Prime Minister Vladimir Putin investigators had found no evidence of a technical malfunction.
"The pilot was informed of severe weather conditions, but nonetheless made a decision to land," Bastrykin said.
Putin went to Smolensk Sunday for a ceremony before the return of Kaczynski's body to Poland, and Russian soldiers carried his coffin as a band played the Polish and Russian national anthems.
Thousands of Poles continued to file into the Presidential Palace past wreaths and red, green and yellow votive lights and descended on churches to pray for the victims.
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