Acting President Bronislaw Komorowski set the date for the election, BBC News reports.
Komorowski and the late leader's brother Jaroslaw Kaczynski, the head of the conservative Law and Justice party, are the early favorites to win the vote.
A run-off will be July 4 if no candidate grabs at least 50 percent of the June 20 poll.
Kaczynski and his wife died in a plane crash April 10 in which 94 other people also perished.
The victims included politicians, military leaders, church officials, the country's national bank chief, the head of Poland's Olympic Committee and relatives of those killed in the World War II Katyn massacre. Kaczynski and his party were to attend a memorial ceremony for the 20,000 Polish slain by Soviet's forces in 1940.
When the 26-year-old Tupolev Tu-154 airliner tried to land in Smolensk despite thick fog, it crashed and burned, killing everyone on board.
Russian Prime Minister Vladimir Putin heads an investigation into the crash. Initial reports suggest a pilot error.
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