SAN FRANCISCO — Yahoo Inc.’s embattled chief executive, Marissa Mayer, who last month disclosed a hack that exposed at least 500 million accounts, is facing a fresh round of questions about the company’s privacy safeguards after a report that she let the US government secretly scan hundreds of millions of user e-mails.

“Their brand equity is going from bad to worse,’’ said Sameet Sinha, an analyst at B. Riley. “You have one of the weakest Internet brand names. People are disconnecting — now that disconnection is going to accelerate.’’

On Wednesday, Yahoo disputed a Reuters report from a day earlier that said the company built a software program to scan customers’ incoming e-mails for US intelligence agencies, saying the story was “misleading’’ and that “the mail scanning described in the article does not exist on our systems.’’

It’s a sensitive time for Yahoo, which in July agreed to sell its Web businesses to Verizon Communications Inc. for $4.8 billion after years of trying to jump-start sales growth. Though consumers and advertisers had been flocking to newer rivals such as Google Inc. and Facebook Inc., the company still touted more than 1 billion monthly users, many of them on Yahoo’s e-mail systems. When the companies announced the deal, which is set to wrap up early next year, Mayer said a priority was “seeing the transaction through to closing and protecting the value in our equity stakes.’’

According to the Reuters report on Tuesday, Yahoo complied with US government orders to scan hundreds of millions of Yahoo Mail accounts at the behest of the National Security Agency or Federal Bureau of Investigation. Intelligence officials wanted Yahoo to search for a set of characters, and that could mean a phrase in an e-mail or an attachment, according to the story, which cited anonymous sources. Reuters reported Wednesday that the lead European regulator on privacy issues for Yahoo, Ireland’s Data Protection Commission, plans to make inquiries about whether EU citizens’ data had been compromised.

“We narrowly interpret every government request for user data to minimize disclosure,’’ Yahoo said in its response.

The New York Times on Wednesday reported that Yahoo was ordered by the United States to search incoming e-mails for the digital signature used by a foreign terrorist organization, citing a government official it didn’t identify. The firm used a version of its existing system that scans for spam, malware, and child pornography to comply with the order, and the collection is no longer taking place, the Times said.

The report Tuesday drew sharp rebukes from critics, who said government officials were asking for too much information — and questioned whether Yahoo did enough to resist the requests.

“Based on this report, the order issued to Yahoo appears to be unprecedented and unconstitutional,’’ Patrick Toomey, an attorney with the American Civil Liberties Union, said in a statement Tuesday. “It is deeply disappointing that Yahoo declined to challenge this sweeping surveillance order, because customers are counting on technology companies to stand up to novel spying demands in court.’’

Following the report, Yahoo e-mail rival Alphabet Inc., owner of Google and its popular Gmail program, said it never received such a request, but that if it did, it would say, “no way.’’

Verizon declined to comment on the newest report.

“If I were them, I would say, OK, give me a list of all the things that went wrong over the last three, four, five years,’’ Sinha said. “Verizon knows there’s going to be some churn, but wants to control the churn.’’

Technology companies came under fire in 2013 after NSA contract worker Edward Snowden revealed classified documents that outlined US government surveillance programs, including some that involved Internet and telecommunications companies assisting agencies in collecting data from private citizens.

Yahoo’s new statement used carefully chosen words, said Jeff Pollard, an analyst at Forrester Research. He said Yahoo could have been bolder in its assertion.

Still, Avivah Litan, an analyst at Gartner, said she believed Yahoo’s contention that it did a minimal amount of “extra’’ scanning requested by the government.