The visit, meant to demonstrate the 27-nation bloc's solidarity with Kyiv amid Russia's ongoing invasion, comes as a host of newly appointed senior EU officials take charge on December 1.
Costa, a former prime minister of Portugal, wrote on the X social media platform that the European Union "has stood by the side of Ukraine" from day one of the war.
"From day one of our mandate, we are reaffirming our unwavering support to the Ukrainian people," he said.
Kallas, a former prime minister of Estonia and a fierce critic of Russia, posted on X: "In my first visit since taking up office, my message is clear: the European Union wants Ukraine to win this war. We will do whatever it takes for that."
EU Enlargement Chief Marta Kos, a Slovenian former diplomat who joined Costa and Kallas on their visit to Kyiv, wrote on X that she was honoured to be in the Ukrainian capital on her first day in the new role.
"We are here with a powerful message: Ukraine you can count on Europe’s unwavering and strong support on your path to freedom, peace and a fully European future," she said.
Russia invaded Ukraine by land, air and sea on February 24, 2022, starting the largest military conflict in Europe since World War II.
Sunday is day 1,011 of Russia's war on Ukraine.
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Source: IAR, PAP, Reuters, ukrinform.net