By Friday, the mayor remained unmoved and said he had no intention of reinstating her. “Amy made a statement, she decided on her own — I didn’t ask her — that she was going to resign, and we accepted her resignation,” he said in an interview.

He said he had seen Ms. Ryan on television saying she would not ask for her job back. “So that’s pretty much the story,” he said.

Her staff had learned a year ago that one of the prints was missing but did not tell her until April. A few days later, when she learned the second piece of art was missing, she reported the losses to the mayor and the police. It is not clear why the staff did not inform her immediately, but Ms. Ryan said this was an “egregious failure of communication” that she was trying to get to the bottom of. The mayor told The Boston Globe that the staff’s failure to tell her earlier raised questions about her leadership.

Mr. Walsh said in the interview on Friday that he was still skeptical about other items reportedly missing at the library, namely, some gold coins from a cornerstone laid in 1855 and sheets of music. The library said those items were missing before Ms. Ryan took the helm in 2008.

“I don’t know how somebody justifies or says that they were missing long before they came here seven years ago and just found out seven years later that they were missing,” the mayor said.

Some people who have worked with Ms. Ryan said her resignation was an unjust capstone to a stellar career, which began at the public library in Minneapolis.

“I think it sucks, frankly, that Marty accepted her resignation and doesn’t seem open to reconsidering,” the novelist Dennis Lehane (“Mystic River,” “Gone, Baby, Gone”) wrote in an email to The New York Times. Until recently, Mr. Lehane served as a library trustee. “It depresses me to know she’s no longer running that ship,” he said.