The royals had a brief exchange as the Queen greeted the US president at a Nato reception on Tuesday.
Footage circulated on social media showed the monarch, stood alongside Prince Charles, turning towards her daughter as she stood a few feet away from the royal receiving line.
The Princess Royal then shrugs and says, “It’s just me”, to signal there are no more dignitaries for her mother to greet – prompting laughter from Mr Trump. Gesturing behind her to members of the royal household, she adds: “And this lot”.
The clip prompted speculation online that Princess Anne had been “scolded” for refusing to join her mother in meeting the president and first lady Melania.
The royal also featured in another video filmed at the Nato reception in which several world leaders appear to make fun of Mr Trump.
British prime minister Boris Johnson and Canada’s Justin Trudeau were seen smiling as they seemingly comment on their American counterpart’s idiosyncratic approach to international diplomacy.
French president Emmanuel Macron, Dutch PM Mark Rutte and Princess Anne also take part in the jokey and exasperated-sounding conversation, captured by a camera they seem unaware of.