Before flying off to the summit in the Portuguese city of Porto, Mateusz Morawiecki said: "I will be speaking very strongly on this matter and we will strive to convince the richest countries which are also patent holders to make these patents available."
He added: "This is needed to eliminate the epidemic across the world."
European Commission President Ursula von der Leyen responded by saying she welcomed Morawiecki's call to step up efforts to share COVID-19 vaccines worldwide.
She wrote on Twitter: "I look forward to working with Mateusz Morawiecki to share vaccines with neighbours and partners, including with our friends in the Eastern Partnership."
In a reversal of Washington's position, US President Joe Biden on Wednesday voiced support for waiving intellectual property rights for coronavirus vaccines.
Focus on social issues
European Union leaders meeting in Porto were expected to declare they will pay attention to social issues, welfare, equality, jobs and education as the 27-nation bloc emerges from the COVID-19 pandemic, the Reuters news agency reported.
Morawiecki said he would highlight the "Polish social model" at the EU summit starting on Friday. He added that this model, which puts an emphasis on the role of the family, has led to a shift towards greater social justice.
Amid a fall in coronavirus infections in Poland, the government earlier this week allowed shopping malls, DIY stores and museums to reopen. It plans to gradually ease a swathe of other lockdown rules this month.
Poland on Friday reported 6,047 new coronavirus infections and 453 more deaths, bringing the country's total number of cases during the pandemic to 2,824,425 and fatalities to 69,445.