Zelensky on Friday attended a meeting, via video link, at the Warsaw university where postgraduate European studies are conducted.
University students also took part in a debate with the Ukrainian president.
Zelensky thanked those gathered for their support of his country's defense effort against Russia.
"We are fighting for Europe and the next generations," he said. "We must guarantee the end of the occupation of all Ukrainian territory and we need global guarantees."
'Russia is implementing a genocidal policy'
Zelensky also said in his speech that "peace, security, freedom, democracy, protection of human rights, and social justice are things that should be fought for decisively, showing leadership, especially when these values are threatened by totalitarian systems."
He added: "Now there is a war going on in Europe, and Russia is implementing a genocidal policy. That is why it is important to continue the struggle for the preservation of European values and the institutions that protect them."
'No other way than to win the battle for Europe'
He told the gathering in Warsaw's Natolin district: "You and I have no other way than to win the battle for Europe. The same way as we have united Europe. In the same way, we are strengthening Europe. In the same way, we guarantee freedom and security to Europe. Long term. Of course, with Ukraine as part of the European Union."
In his speech, Zelensky announced the start of work to create a College of Europe in Kyiv, Polish state news agency PAP reported.
He said: "Ukraine's participation in European affairs must increase, we must have specialists in these issues, so I am glad that there are also Ukrainian students in Natolin, I am sure that they will represent Ukraine with dignity in EU institutions."
Source: PAP, president.gov.ua