The White House announcement came about six hours before Obama was scheduled to depart on the overnight flight. Obama called Poland's acting president, Bronislaw Komorowski, with the news that the trip was off, citing fallout from the volcano in Iceland.
Kaczynski and 95 others, including numerous lawmakers, the central bank governor, the commanders of the country's armed forces and the head of its Olympic committee, died in a plane crash April 10 near Russia's Katyn forest, site of a World War II massacre of Polish officers.
Obama said in a statement that he would support the Polish people in any way he can as they recover from the loss of so many leaders and officials.
He said the late president and others who died were close friends of the United States. "The American people will never forget the lives they led," Obama said.
All airports in Poland were closed Saturday to flights above the cloud level of 20,000 feet because of the ash cloud, including Balice in Krakow, where most of the dignitaries were expected to arrive Sunday morning, said Grzegorz Hlebowicz, spokesman for Poland's aviation authorities.
Scientists say that because the Icelandic volcano is situated below a glacial ice cap, the magma is being cooled quickly, causing explosions and plumes of grit that can be catastrophic to plane engines.