In the meeting with Japan's Prime Minister Shinzo Abe at the mogul's Trump Plaza residence, Ivanka -- a model-turned-business executive -- was seen seated as the group conversed in the opulent reception room.
Media were shut out of the gathering in Manhattan, but images released by the Japanese government also showed Ivanka and her husband, real estate developer and publisher Jared Kushner, standing and chatting with Abe.
Ivanka and Kushner, both 35, have emerged as key advisers to Trump, who shocked the world by beating Democrat Hillary Clinton in the November 8 election.
Abe told reporters afterwards that the encounter convinced him the US president-elect was someone "in whom I can have great confidence".
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"We were able to have a very candid talk over a substantial amount of time. We held it in a very warm atmosphere," he said. "Without confidence between the two nations, our alliance would never function in the future."
Also seen standing in one of the photos, amidst the gilt and chandeliers of Trump's skyscraper, was former general Michael Flynn, who has reportedly been offered the post of national security adviser.
"It's quite unusual to see a family member attending the first encounter between two leaders even if it's informal," said Yoshinobu Yamamoto, a professor at the University of Niigata Prefecture,
"It indicates that she would be playing some important role in the Trump administration," he added.
"But it's no surprise to see her there as she has already been involved in politics. Anyway, that's the Trump way."
The Tokyo Sports newspaper carried an article headlined "Trump daughter-blonde beauty Ms Ivanka the next ambassador to Japan!?" on its website last Saturday.
It cited unidentified overseas media as having reported before the vote that Trump had secret plans to appoint her ambassador, replacing current envoy Caroline Kennedy who is the daughter of assassinated US president John F. Kennedy.
"I don't think the possibility that Ivanka would be an ambassador to Japan is zero, but it's too early to say," said Yamamoto.