"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.
"We should use shock therapy to sober up the Americans. In this case, the Americans will speak about the need to resume dialogue. There is no other option"
The United States is concerned about the current crisis in the relations with Russia and suggests returning to reasonable policies to avoid a nuclear war