The country had been due to hold a presidential election in October, when Kaczynski, a conservative, was expected to run against Komorowski, a liberal.
Poland has moved to fill important positions in the state administration, after dozens of political and military leaders were among the 96 killed in Saturday's crash.
'Public show of grief'
Kaczynski and his entourage had been travelling to mark the 70th anniversary of the massacre of Polish officers by Soviet secret police near Smolensk when his plane went down in thick fog.
Poland has entered its third day of mourning for the victims, with a funeral expected to be held on Saturday.
Jonah Hull, Al Jazeera's correspondent in Warsaw, said there was a "very public and open show of grief for what has been an enormous shock in Poland".
"The presidential palace has become a focal point for that public grief, a shrine it has become with an ever-growing sea of candles brought and lit by people as a sign of respect and remembrance.
"Hundreds of people still here, it is a normal working day but that hasn't stopped people coming," he said.
Parliament on Tuesday prepared to hold a special observance in memory of the politicians killed, as the body of Maria Kaczynska, the president's wife, was returned home from Russia.
Kaczynska's body, in a wooden casket draped with Poland's white-and-red flag, arrived in a military plane shortly after 10:30 local time at Warsaw's Okecie airport.
It was greeted by her only child, daughter Marta, and Jaroslaw Kaczynski, the twin brother of the late president.
Russian investigators have suggested human error may have been to blame for the crash, saying on Monday that there were no technical problems with the Soviet-made plane.
Alexander Bastrykin, Russia's chief investigator, said the flight recorders revealed that while there were "no problems with the plane", the pilot decided to land despite warnings about bad weather conditions.
Polish media have speculated that the pilots were pressured by people aboard the jet to land quickly so as not to miss a memorial ceremony for thousands of Poles massacred in the second world war.
But Andrzej Seremet, Poland's chief prosecutor, said on Monday there was no evidence to support the claim.
Investigators in Poland are expected to listen to cockpit conversations from the flight recorders, also known as "black boxes", to see if there were "any suggestions made to the pilots" from other people aboard the aircraft.
Poland has declared a week of national mourning following the disaster.