ATLANTA — Gov. Pat McCrory of North Carolina is expected to respond on Monday to the Justice Department’s warning that a new state law limiting the rights of transgender people is illegal, after he and the federal government failed to reach an agreement that would have allowed him to postpone his reply.

Mr. McCrory said that he could not assent to the Justice Department’s condition for a one-week extension — an acknowledgment by him that the law is discriminatory — and would answer by 5 p.m. on Monday.

“I’m not going to publicly announce that something discriminates, which is agreeing with their letter, because we’re really talking about a letter in which they’re trying to define gender identity, and there is no clear definition of gender identity,” Mr. McCrory, a Republican who is seeking re-election this year, said on “Fox News Sunday.” “It’s the federal government being a bully.”

The governor said that he was “discussing all of our legal options, all of our political options,” and he appeared to rule out the possibility that he would take some kind of independent action to undo the law, or at least limit its enforcement, as some people have suggested.