The appeal was made in a letter to European Council President Charles Michel ahead of a European Union video summit on the pandemic later this week.
“Europe's timely access to sufficient vaccines remains an unsolved challenge,” the leaders wrote.
They added: “In spite of the unprecedented speedy development of new high-quality vaccines, production difficulties are ongoing and lead to major delays. In combination with the emergence of new COVID variants, this risks jeopardizing our path to full recovery and normal life.”
The EU summit takes place on Thursday and Friday.
'Paying a huge price'
Polish Prime Minister Mateusz Morawiecki last week called on the European Union's executive to use its sway to ensure the timely delivery of COVID-19 vaccines amid delays in supplies from drug producers.
"Europe is a powerful market that has been hard hit by COVID-19," Morawiecki said. "Every day we are all paying a huge price for displaying a weakness toward drug makers. We can't stand aside and watch the next waves of infections engulf us."
The European Union, of which Poland is part, has struck deals to secure vaccines from Pfizer-BioNTech, AstraZeneca, Moderna, CureVac, Sanofi-GSK, and Johnson & Johnson.
Morawiecki's chief of staff, Michał Dworczyk, said last month that a move by Pfizer to reduce the supply of COVID-19 shots had forced Poland to modify its vaccination plans.
Poland on Tuesday reported 6,310 new coronavirus infections and 247 more deaths, bringing its total number of cases during the pandemic to 1,648,962 and fatalities to 42,436.
Nearly 2.76 million COVID-19 vaccine shots have been administered in Poland so far, officials said on Tuesday.