NEW YORK — A federal judge did not make a decision last week on Google’s controversial move to digitize millions of out-of-copy books, prolonging a years-long battle to build the world’s biggest online library.

The search giant’s long and bumpy journey into digital book search and publishing stands in stark contrast to its steady march into a remarkable list of other Web-affected industries. In the past two months alone, Google began selling its own cell phone, introduced a controversial social networking feature to its e-mail program and said it would dip into the world of telecommunications with tests for ultra-fast fiber optic networks.

U. S. District Court Judge Denny Chin told a packed courtroom on Thursday that he will listen with an “open mind” to arguments for and against Google’s settlement with some authors and publishers over the right to scan and publish titles.

Walking into a courtroom at the U. S. Court of the Southern District New York with a tall stack of comments submitted by parties, Chin said: “To end the suspense, I’m not going to rule today. There’s too much to digest.

“However I come out, I want to write an opinion that explains my reasoning. I will listen carefully, and I may ask a few questions.”

The court received more than 500 comments ahead of the hearing, the purpose of which is to determine the fairness of a $125 million settlement struck in 2005.

The judge will hear 28 comments during the hearing — nearly all of which are from opponents of the deal who say it violates copyright laws, gives Google an unfair edge over competitors and raises privacy concerns.

The fairness hearing is being conducted after a yearlong delay and two opinions by the Justice Department that criticize the deal for potentially edging out rivals in the book publishing and search markets. In comments submitted to Chin, Justice said the deal is still a “bridge too far.”

Critics, including some library groups, some authors and competitors such as Microsoft and Amazon, argued that if approved, Google’s deal would violate copyright laws and give the search engine exclusive rights to many titles, just as readers increasingly turn to electronic reading devices over paper. Privacy advocates warn that nothing in the settlement would protect users’ personal habits and information from being tracked for behavioral advertising.

Google, which hadn’t presented its own arguments to the judge, has emphasized that the number of books included in the settlement is a small portion — about 3 percent — of all titles in the world. In it, users can look at about 20 percent of a title online for free and if they choose, they can eventually purchase it from Google.

Some libraries, including that of the University of Michigan, praised the deal in the hearing. They say most of the books in the settlement are scholarly works that are collecting dust on university bookshelves and would not otherwise be read. Minorities and advocates of the blind say that by making such publications available online, people will have easier and cheaper access to works that are difficult to get today. Digital information can be presented in auditory, large print or refreshable Braille formats.

Like Google’s forays into the cell phone, video and map markets, the book project is intended to support the company’s core business — Internet search. The more people come to the Web to search for information, the more money Google can make from online advertising.

“The proposed Google book settlement is not a philanthropic effort to bring literature into the 21st century and bridge a literary divide,” opponents Microsoft, Amazon and library groups wrote in a recent filing through the Open Book Alliance. “This de facto exclusive license will provide Google with an enormous advantage over its search competitors.”

The settlement, while limited, is part of Google’s more ambitious effort to put all the world’s books online and eventually be the main source for searching and buying titles as readers increasingly turn to their computers and gadgets for books. Critics say the project gives exclusive rights to Google to scan and publish those works online—which would put competitors at a disadvantage.

“If approved, this settlement would improperly destroy potentially millions of absent authors’ exclusive copyrights and would give Google an unfair monopoly that is not in the public interest,” Daniel Fetterman, an attorney for Consumer Watchdog, said in a press statement.

Privacy advocates argue that the deal has the potential to put users’ private information and online habits at risk. Data is automatically collected about a user’s search habits on Google Book Search. Some critics urged the judge to reject the settlement unless Google promises it won’t hand over personal data to commercial third parties or to law enforcement without a warrant or court order, said Aden Fine, an attorney for the American Civil Liberties Union.

“The traditional protections for readers that we’ve always had in bookstores and in libraries should apply to digital libraries as well,” Fine said.