"The president of the Diet (lower house of parliament) Bronislaw Komorowski has taken the decision to call elections for the president of the republic of Poland on June 20," the parliament's press service announced.
Under Polish law, a possible run-off second round would be held on July 4.
Parliamentary speaker Komorowski has been acting president since Kaczynski and his wife were killed along with 94 others when the presidential jet crashed on April 10 near Smolensk, western Russia.
The presidential delegation was on its way to ceremonies marking the 70th anniversary of a Soviet World War II massacre of Polish officers in the nearby Katyn forest.
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The late president and his wife were buried on Sunday in Krakow's Wawel castle cathedral, the ancient seat of Polish kings.
A presidential ballot had been due by October with Komorowski, a liberal, expected to run and win in the first round against the conservative Kaczynski, whose popularity has flagged since his 2005 victory.
Komorowski was legally bound to announce a ballot date within two weeks of the president's death on April 10. Under the constitution the snap presidential ballot must be held within 60 days of the election announcement.
Kaczynski's identical twin brother Jaroslaw, who was premier from 2006-7 in tandem with his presidency, may take his sibling's place, although he has made no public statement on his political plans since the crash.
His opposition Law and Justice (PiS) party is to meet on Saturday to decide on a presidential candidate. Political parties are bound under the constitution to present their presidential candidates to the state elections commission by Monday.
As of Wednesday, only Bronislaw Komorowski, the candidature for Poland's governing Civic Platform (PO) party, was a clear candidate.
The ex-communist social democrats were scrambling for a candidate after Poland's one-time defence minister Jerzy Szmajdzinski died in the Smolensk crash.
A conservative nationalist, Lech Kaczynski was a divisive figure at home and abroad, but the mood since his death has been one of grief across the political spectrum.
