The Academy, which has pledged to double its numbers of women and minority members by 2020, apologised, saying that it "regrets that any aspect of the Oscar telecast was offensive.
"We are committed to doing our best to ensure that material in future shows be more culturally sensitive" it added in a statement.
February's Oscar ceremony was hosted by black comedian Chris Rock, who lambasted Hollywood for its lack of diversity and in particular the lack of African-Americans among the 20 acting nominees for a second straight year.
The letter writers gave no details of their objections. But members of the Asian community were upset after the show at a skit in which Rock introduced three Asian children as Academy accountants.
In another part of the ceremony, British comedian Sacha Baron Cohen, appearing as a presenter, made an apparently off the cuff remark about the size of Asian genitalia.
"We'd like to know how such tasteless and offensive skits could have happened and what process you have in place to preclude such unconscious or outright bias and racism toward any group in future Oscars telecasts," said the letter.
In addition to Life of Pi director Lee, the letter was signed by former Grey's Anatomy star Sandra Oh, France Nuyen of The Joy Luck Club as well as documentary makers and producers, all of whom are already Academy members.
- AFP