A bystander told a US publication that David apologised on Victoria's behalf, saying: "Victoria really wanted to come, but she is just so tired at the moment. She sends you both lots of love."
David met the Duke and Duchess of Cambridge at a reception held by the British-Consul General, Barbara Hay.
Prince William reportedly replied: "Don't be silly. Please send her all our love and tell her good luck with it all."
Victoria is thought to be due to give birth to the couple's fourth child this weekend.