The two leaders also spoke about strengthening sanctions and pressure on Russia, as well as the prospect of peace, he added.
Zelensky said in a post published to his verified Twitter account that he and Scholz had "productive talks."
"We look forward to Germany's further assistance on Ukraine's path to full EU membership," he added.
Some background: The meeting between Zelensky and Scholz follows earlier tensions between Kyiv and Berlin. In recent months, the German government and Scholz came under pressure from Ukraine and politicians at home for not doing enough to help Ukraine defend itself against the Russian invasion.
But at the end of April, Germany agreed to deliver Gepard anti-aircraft tanks to Ukraine, and later said it will supply Kyiv with seven self-propelled howitzers.
Last week, Ukrainian Foreign Minister Dmytro Kuleba said Germany had now moved in "the right direction."
Kuleba said last Thursday that the decision about Ukraine's membership of the European Union, due to be taken at the European summit at the end of June, will largely define the future of Europe.
''The EU needs Ukraine as much as Ukraine needs the EU,'' Kuleba said.