Zelensky, who met with Duda in the southern-Polish resort town of Wisla, wrote that he and the Polish president also fixed a timetable for future talks.
"Productive talks with my friend Andrzej Duda are in progress," Zelensky wrote. The meeting between both presidents will be continued on Friday.
Earlier, Duda's international affairs aide Jakub Kumoch and the head of the National Security Bureau (BBN), Pawel Soloch, said the Duda-Zelensky talks would focus on regional security, especially Russia's aggressive conduct towards Ukraine.
"Supporting Ukraine is one of the most important priorities of President Andrzej Duda's policy," Soloch added.
According to Soloch, during talks with Zelensky, Duda will also speak about "the possibility of Poland's support for Ukraine, not only in a political dimension, but also a material one."
The BBN head made the statement when asked by Polish public television on Thursday evening whether Poland would offer military support to Ukraine in the context of a Russian buildup of forces at the borders of Poland's eastern neighbour.
Russia has massed tens of thousands of troops on its borders with Ukraine in what Western states fear is the precursor to a new assault on the former Soviet republic. Russia denies it is planning an attack, but says it could take unspecified military action if a list of demands is not met. (PAP)