The election had been scheduled for May 10, but failed to go ahead amid a coronavirus pandemic, which has claimed 965 lives in the country.
"Today, we’re aiming for June 28," Morawiecki told reporters on Thursday.
Incumbent President Andrzej Duda, who is backed by Poland’s governing conservatives, is standing for another five-year term in office and is ahead in the polls.
Polish opposition politician Małgorzata Kidawa-Błońska announced last week she was withdrawing from the race to make room for a candidate who would have a better chance of defeating Duda.
The opposition Civic Platform (PO) party then chose Warsaw Mayor Rafał Trzaskowski as its new pick for head of state.
Polish deputies last week approved plans to conduct the presidential election via a mixed system of postal and traditional in-person voting.
(pk)