ALBANY — State education officials expressed doubt today about whether the testing firm Pearson, which has several contracts in New York, can handle its expanding workload.

“Obviously, the public is starting to question, I think, very aggressively with us whether or not they’re able to manage all of the things they’ve taken on,” New York State Board of Regents Chancellor Merryl Tisch said of Pearson, whose subsidiary testing company NCS Pearson, Inc. has a five-year, $32 million contract to create tests for the state.

Tisch, who has criticized the testing company before, was responding to Pearson’s latest misstep in test administration. On Friday, the New York City Department of Education said nearly 5,000 students were told they were ineligible for the city’s Gifted & Talented programs when they actually should have made the cut. Three separate errors took place during test grading, which Pearson oversaw, department and company officials both said.

Pearson has been in business with the city since at least 2003, securing more than $120 million in contracts to provide publishing materials, professional development services and, more recently, tests. NCS Pearson, Inc. began creating the city’s gifted tests in 2006 and received a new $5.4 million contract last year to continue its work. Pearson agreed to $500,000 in cost reductions and expenses, $80,000 of which will cover communications and outreach to affected families.

Pearson currently has 11 active city contracts worth more than $50 million, according to a review of the city comptroller’s Clearview online database.

The state’s relationship with Pearson is less established. It didn’t start working with Pearson until 2010, when it hired the company to scale the state’s field tests. A few months later, Pearson won a $32 million contract to help the state design new assessments aligned to the Common Core, a deal that runs until December 2015.

Last year, in the first year running the state’s testing program, the company was widely criticized for including exam questions that included nonsensical reading passages and some errors.

Tisch said this year’s English exams, the first to be aligned to the new standards, “had none of the issues that we had last year.” But she said Pearson didn’t deserve all of the credit. Following last year’s issues, the state cracked down on Pearson, ordering the publishing giant to agree to make changes to the way it administers the tests moving forward.

“I’d remind everyone that Pearson didn’t do those alone,” Tisch said. “We had our team working with them and overseeing it. So obviously I’d like them to be able to manage themselves.”

A Pearson spokeswoman said the company is determined to show that it can handle the work it has been hired to do. “We understand these concerns and take them very seriously,” said the spokeswoman, Susan Aspey. “We’re absolutely committed to meeting and exceeding our contract obligations in service to the people of New York.”

Pearson also runs the testing programs of several other states, including Texas, Kentucky, and Illinois. Bronx Regent Betty Rosa said Pearson’s broadening portfolio might be starting to damage what she said had been a good reputation at administering gifted and talented programs for the city.

“They’ve always had a good history with this test,” she said. But, she added, “if you spread yourself out too thin sometimes that’s an issue.”

The criticism comes at a critical moment for Pearson. As states consider whether to adopt Common Core-aligned reading and math tests that are produced by groups of states, Pearson must prove its value or risk losing a major segment of its market. New York State is working with one of the testing consortiums but has not yet committed to administering its tests, which would be available for the first time in 2015.

For now, city officials criticized Pearson but said they were prepared to continue the relationship.

“I have told the company’s officials in no uncertain terms that I expect this will never happen again,” Chancellor Dennis Walcott said in a statement last week. Today, he added, “Pearson is a big company, and what they did was totally unacceptable.”