The New York City department charged with overseeing day care centers routinely failed to test the centers’ water for lead — and for years falsified reports that the tests had been completed, in order for the centers to receive operating permits — according to a sharply worded audit released on Friday by the city comptroller, Scott M. Stringer.

The audit found that the city’s Department of Health and Mental Hygiene had not tested the water from faucets and fountains in 70 of 119 day care centers — even though the health code mandates that drinking water at day care centers be tested for lead and fixed if the levels are unsatisfactory.

Of the 49 day care centers that had been tested, five had “unacceptable” levels of lead, the audit found, though the levels were later brought to acceptable levels. The audit suggested that thousands of children were put at an increased risk of lead exposure.

The audit also found that records had been altered to indicate, incorrectly, that satisfactory water test results were logged for the 70 centers that had not been tested.

“The fact that the department of health directed its employees to enter false information in an official database is a blatant violation of public trust,” Mr. Stringer said in a statement.

The comptroller’s office presented an email from 2011, in which a manager at the Bureau of Child Care, a division of the Department of Health and Mental Hygiene, instructed a group of staff members to “enter Water Lead Test Negative” in a computerized database “in order to issue permits” on an interim basis.

“By falsely recording that lead tests were complete, the agency was able [to] bypass its own system requirements to issue permits for day care centers,” a release from the comptroller’s office said.

City Hall officials characterized the findings as misleading and said that no children had been harmed. “It is a blatant mischaracterization to claim the agency systematically falsified documents based on a single email from 2011,” Aja Worthy-Davis, a spokeswoman for the mayor’s office, said.

Ms. Worthy-Davis also pointed to the audit’s relatively small sample size; the department oversees about 2,300 day care facilities.

The specifications in the city’s health code for testing water in day care centers do not require that the centers are tested before they open. However, the health department’s database was changed in 2011, to prevent the issuing of permits to centers that had not been tested for lead, Mr. Stringer’s release said.

Health department officials described a practice of entering incorrect testing information as a bureaucratic workaround that adhered to the city’s health code. The intent was to give day care centers 60 days to submit lead test results, and not delay issuing permits for “programs that were in good standing.”

The comptroller’s office said it did not find evidence that anyone had followed up to test the centers where staff had falsely reported that testing occurred.

The report comes amid heightened concerns about lead and other pollutants in drinking water, after national outrage over lead contamination in Flint, Mich., and a public health emergency in Hoosick Falls, N.Y., after the disclosure that toxic chemicals were found in the water supply there.

The outlook was better in New York City, where water has not been a major cause of lead poisoning, according to the Department of Health and Mental Hygiene. Out of the 840 children under the age of 6 found with elevated lead in their blood in 2014, none tested positive from lead in water, according to the most recent statistics from the department.

“We want to be clear: our kids are not at risk,” a health department spokesman, Christopher Miller, said in a statement.

Mr. Miller said the city has amended the issues brought up in the audit. All of the day care centers under the city’s purview, including the 70 identified in the audit, have now been tested for lead in the water, he said. The city also said it planned to start posting the results of each location’s water tests online.

Ms. Worthy-Davis said that the lack of clarity in terms of lead-testing protocol for day care centers predated the de Blasio administration, and she noted that “a bureaucratic process made testing standards vague beginning in 2011.”

This month, the health department proposed a change to the health code that would require lead testing at new centers within 30 days of their opening. They would also be required to undergo testing every five years.

But a spokesman from Mr. Stringer’s office said the changes only came about from the results of the auditing process, which were given to the city — and included a response from the health department in the written report — before they were released to the public.

“It should not take an audit to ensure that a city agency is doing its job to protect our kids,” Mr. Stringer said in a statement.