The actor who portrays Apu Nahasapeemapetilon, the thickly accented convenience store owner on “The Simpsons,” said Tuesday that he would be “perfectly willing and happy to step aside” as the voice of the character.

For nearly 30 years, Hank Azaria has been the voice behind the stingy Indian-American owner of the high-priced Kwik-E-Mart in Springfield, the show’s fictional town. Mr. Azaria, who is white, gave Apu a pronounced Indian accent, which, along with the character itself, has come under intense criticism in recent months as a racist stereotype.

In December, Mr. Azaria said that he found the situation “upsetting” and that there were “a lot of things to think about.” But on Tuesday, in an interview with Stephen Colbert on “The Late Show,” he offered his fullest response yet to the criticism, which started with the debut last fall of the documentary “The Problem With Apu.”

The documentary’s producer, Hari Kondabolu, a comedian of South Asian descent, said in the film that Mr. Azaria’s rendition of Apu was more like “a white guy doing an impression of a white guy making fun of my father.”