Donald Tusk made the statement at a news conference in Warsaw on Wednesday.
Meeting reporters after a Cabinet meeting, Tusk said that April 7 "seems the most likely date" for the local elections.
The prime minister said the government wanted to hold the ballot after Easter, which falls between March 29 and April 1, to ensure voter turnout would be as high as possible.
Tusk said the second, runoff round of the local elections would be organised on April 21.
He added that hopefully Poland's co-governing pro-European parties, Civic Coalition (KO), Poland 2050, Polish People's Party (PSL) and the Left, would contest the local elections as a "single bloc," the rp.pl website reported.
Under the electoral law, Poland's next local elections are due to be organised between March 31 and April 23, 2024, the state PAP news agency reported.
The prime minister also told reporters that later this week Justice Minister Adam Bodnar would outline the Cabinet's plan for "changes to Poland's Constitutional Tribunal."
The plan is designed to help allay the European Union's concerns over democratic standards in Poland, such as judicial independence, under the previous conservative government, according to news outlets.
This would allow Poland access to billions of euros in grants and loans for the country, withheld by Brussels due to these concerns.
Tusk also said on Wednesday the centre-left governing coalition would propose "a list of state agencies to be abolished" and "personnel changes to be made" in the machinery of government, following the eight-year rule of the conservative Law and Justice (PiS) party.
The prime minister said these measures would be unveiled by the end of January, the PAP news agency reported.
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Source: IAR, PAP, rp.pl, interia.pl