"He will be remembered as a respected leader who secured the prosperity of Monaco's people," Bush said in a statement released in Washington by the White House. "Monaco and the United States have long had a special bond of friendship. We extend our deepest condolences to His Serene Highness Prince Albert, to the Grimaldi family, and to all the people of Monaco."
Prince Rainier, whose 1956 marriage to American actress Grace Kelly captured global headlines, died Wednesday following heart, lung and kidney problems. He was 81.
Monaco, located adjacent to France, is smaller than New York's Central Park and is noted for its gambling casino.
Rainier's son, Prince Albert II, will assume the throne.
Bush Wednesday night was in Rome to attend the Friday funeral of Pope John Paul II.