The Republican was asked repeatedly about his comments Tuesday during an impromptu news conference after touring a Caterpillar Inc. facility in the York suburbs.
In a TV interview last week, he said sibling marriage was a better analogy to gay marriage than two children marrying.
Corbett says he has publicly apologized and that his apology was heartfelt. He says he can't control whether people accept it or not.
The first-term governor is up for re-election next year.