The USS Annapolis entered a naval base in South Korea's southern island of Jeju, to load military supplies while on an unspecified operational mission, the South Korean navy said.
The two leaders held a meeting on the sidelines of the NATO summit in Lithuania, during which they also condemned North Korea's launch of an intercontinental ballistic missile.
Zelenskyy expressed gratitude over Seoul's pledge to send de-mining vehicles and aid totaling some $230 million, but said Ukraine wanted anti-aircraft and early warning systems.
The Nuri rocket lifted off from Naro Space Center on Thursday in its third flight after technical glitches caused the launch to be cancelled a day earlier.
Yoon's trip is the first state visit to the U.S. by a South Korean leader in 12 years and will mark the 70th anniversary of a partnership that has helped anchor U.S. strategy in Asia.
It was the first time that Seoul suggested a willingness to provide weapons to Ukraine, more than a year after ruling out the possibility of lethal aid.
Counselors have been trying to build more rehabilitation centers, but requests for government funding are said to fail amid poor awareness about the need for more facilities.
South Korea's defense ministry said the allies have been exploring ways to support Ukraine but declined to confirm specific discussions.
State media KCNA released a commentary criticizing the exercises as "a trigger for driving the situation on the Korean peninsula to the point of explosion."
Lee, chair of the main opposition Democratic Party, faces several charges, including bribery, corruption, breach of trust and conflicts of interests.
