Ukraine is keen to receive advanced fighter jets such as the US F-16 from the West to help fight back Russian invaders and defend itself from air strikes.
Poland is a close ally of Ukraine and helped to galvanise support in the West to supply main battle tanks to Kyiv as part of a coalition of powers.
"Just as your leadership proved itself in the tank coalition, I believe that it will manifest itself in the planes coalition," Mr Zelenskyy said in a speech on a square in Warsaw.
He said Russia would not defeat Europe while Ukraine and Poland were working closely together.
"Poland with you, shoulder to shoulder, we will establish freedom in Europe forever. Tyranny will lose in history when it loses in Ukraine," Mr Zelenskyy said.
He warned against the danger of solidarity fading for Ukraine and said that artillery and tanks should be provided when the battle on the front lines required it.
"Because this is a battle for freedom and it is impossible to win partially," he said.
Poland would be ready to send all its MiG-29 fighter jets to Ukraine “in the future”, said Polish President Andrzej Duda, having already pledged 14 Soviet-made planes to Kyiv.
“I think that in the future we will be able to transfer our whole remaining fleet of MiG-29s to Ukraine, if there is still such a need,” he said.
Mr Zelenskyy and his wife, Olena Zelenska, were welcomed to Poland with military honours, tributes and praise in the leader's first visit since the Russian invasion just over a year ago.
At a welcome ceremony in the courtyard of the royal palace, while Mr Duda and the two first ladies wore formal attire, Mr Zelenskyy was in his signature dark T-shirt and khaki trousers as a show of support for Ukraine’s fighters.
Mr Duda awarded Mr Zelenskyy Poland’s oldest and highest civilian distinction, the Order of the White Eagle, saying it is given to outstanding people in Poland and abroad.
“We have no doubt that your attitude, together with the bravery of the nation, has saved Ukraine,” he told Mr Zelenskyy.
Mr Duda also said Warsaw would seek more security guarantees for Kyiv at a Nato summit in July.
“Today we are trying to get for Ukraine … additional guarantees, security guarantees, which will strengthen Ukraine's military potential,” Mr Duda told reporters after talks with Mr Zelenskyy, adding that Poland supports full Nato membership for Ukraine.
More than 1.5 million Ukrainians have registered with the Polish government since the war began, joining large numbers that had already arrived for work.
The exact number of Ukrainians in Poland at any given moment is almost impossible to measure, especially with many going back and forth.
Since Russia invaded in February 2022, Mr Zelenskyy has visited Washington, London, Paris and Brussels.
While Mr Zelenskyy’s previous trips were part of his push for war planes and for Ukraine’s EU and Nato membership, and his visit to Washington last December was to shore up US political support, the journey to Warsaw was intended primarily to thank a country that has been an international cheerleader for Ukraine.
Poland, on Nato’s eastern flank, feels especially threatened by Russia and has been one of the leading advocates for providing military aid.
But Mr Zelenskyy’s visit comes at a delicate time, with Polish farmers becoming increasingly angry because Ukrainian grain entering Poland has created a glut, causing prices to fall.
The grain is meant to be stored and transported through Poland to reach international markets, but farmers in Poland say the grain is instead staying there, taking up space in silos and entering local markets.
Romanian and Bulgarian farmers say they are facing the same problem.
Mr Przydacz acknowledged in comments to reporters that the issue has caused tensions and said it would be a topic of the talks on Wednesday.
An hour before Mr Duda was to welcome Mr Zelenskyy, Poland's Agriculture Minister Henryk Kowalczyk, who has been the focus of the farmers' anger, resigned from his post.
The US on Tuesday unveiled $2.6 billion more in military assistance for Ukraine, including three air surveillance radars, anti-tank rockets and fuel tankers. The US has now provided more than $35 billion in military aid to Ukraine since Russia's invasion.
“The main thing is not to lose time, not to lose the chance we have. Act now, help now,” Mr Zelenskyy told the US National Governors Association by video link.
Tens of thousands of Ukrainian civilians and soldiers on both sides have been killed in what Russia calls a “special military operation” but the West views as an unprovoked assault to subdue an independent country.
The battle for the ruined eastern city of Bakhmut has been one of the bloodiest of the conflict, with heavy losses on both sides and the small city largely destroyed.
The founder of Russia's Wagner mercenary force, Yevgeny Prigozhin, recently claimed that his forces had captured the mining and logistics centre.
Ukraine has repeatedly denied that Russians control the city, while acknowledging they have taken at least half of it.
“In the Bakhmut sector, there was no let-up in enemy actions aimed at storming the city of Bakhmut. At least 20 enemy attacks were repelled here alone over the past 24 hours,” the Ukrainian general staff said in a report on Facebook.
Elsewhere, Russian media reported that a Ukrainian drone crashed near the Zaporizhzhia nuclear power plant, as the chief of the global nuclear watchdog was expected in Russia for talks about the plant's security.
International Atomic Energy Agency head Rafael Grossi was due to travel to Russia's Kaliningrad region on Wednesday, a week after visiting the Zaporizhzhia plant in southern Ukraine, which is controlled by Russian forces.