J.D. Vance Claims Ukraine Supporters Chased Him, 3-Year-Old Daughter

J.D. Vance says he and his daughter had a scary run-in with protesters Saturday afternoon ... 'cause he claims a few overzealous supporters of Ukraine chased them down.

The vice president described the alleged interaction on X ... writing that while walking with his three-year-old daughter a group of "Slava Ukraini" protesters yelled at and followed them -- which made his daughter anxious and scared

Vance says he tried to defuse the situation by speaking with the protesters in hopes of stopping them for harassing her -- a move which he says worked, by and large.

Vance called the conversation "mostly respectful" ... before adding that anyone chasing after a kid as part of a political protest is a "s*** person."

Worth noting ... there's no video of the incident VP Vance is describing. We've reached out for further clarification on what went down from the Secret Service -- so far, no word back.

Vance and his wife Usha share three children -- Ewan, Vivek and Mirabel -- and the latter two have made multiple appearances at big political events. Ewan has mostly avoided the spotlight.

As you know ... tension regarding the relationship between the United States and Ukraine have exploded in recent days -- especially after the fraught meeting between Vance, U.S. President Donald Trump and Ukraine's President Volodymyr Zelensky.

Remember, Vice President Vance told President Zelensky he needed to be more grateful to President Trump because he was trying to save Ukraine ... the beginning of a spiral that led to a shouting match, and eventually saw Zelensky booted from the White House.

Pro-Ukraine protesters gathered in Vermont to demonstrate while Vance went on a skiing trip in the state after the meeting ... and, one irate person even asked him what it feels like to be "Putin's puppet."