The April 10 plane crash killed not only Kaczynski of the nationalist conservative Law and Justice party, but also Jerzy Szmajdzinski, the candidate for the Democratic Left Alliance. Both parties have been deep in mourning and have not yet chosen new candidates.
The date of June 20, announced by speaker Bronislaw Komorowski, was widely expected. Komorowski is the acting president and will be the candidate for his moderate, pro-EU party Civic Platform.
If no candidate musters at least 50 percent, a second round must be held two weeks later, on July 4.
In Poland, most power lies with the government, which is elected separately from the president. The president has mainly a ceremonial role, though he can veto legislation and as commander in chief he has some influence over foreign policy.
Elections were originally to have been held this autumn but were moved up following Kaczynski's death in the crash in western Russia that also killed his wife and 94 others, including many of the nation's civilian and military leaders.
Komorowski was chosen as Civic Platform's candidate in late March, two weeks before the president's death thrust him into the role of acting president.
His main rival in the election is expected to be from Law and Justice, the late president's party. Polish media reports say that Law and Justice members are encouraging the party leader, Kaczynski's twin brother Jaroslaw Kaczynski, to run.
Recent opinion polls show that Komorowski would win in a race against Jaroslaw Kaczynski, a former prime minister with a polemical style that often put Poland at loggerheads with the European Union.
A poll released Wednesday in the Rzeczpospolita daily showed that should Jaroslaw run, he would win 26 percent of the votes to Komorowski's 49 percent, with much lower support going to candidates from several smaller parties.
The poll, by GfK Polonia, questioned 1,000 Poles on Tuesday. It had a margin of error of plus or minus 3.2 percentage points.
