"She is an exemplary daughter, we're very proud," the prince said, carrying his third daughter on a white embroidered pillow.
"We had a relaxed night and the delivery went very well," Willem-Alexander said at a nationally televised news conference. "We can't wait to show her to (her elder sisters) Amalia and Alexia."
The girl, who is fourth in line to the Dutch throne after her father and two sisters, was born just before 10 p.m. (2000 GMT) Tuesday night at the Bronovo Hospital in The Hague, according to a Royal House statement.
She weighed in at 4.2 kilograms (9.1 pounds) and was 52 centimeters (20.5 inches) long. Her name has not been released.
A former investment banker, Maxima married Prince Willem-Alexander, the oldest son of Queen Beatrix, in 2002.
Russian President Vladimir Putin said at the meeting of the Valdai Discussion Club that Russia will never initiate military actions, including with the use of nuclear weapons