Some residents are frustrated at how long it took the city to admit the problem. “I applaud the city for now, finally, acknowledging the issue, but they first denied it,” said Bishop Jethro C. James Jr., the senior pastor at Paradise Baptist Church. “The denial was an insult to the citizenry.”

Candice Grant, 25, an administrative assistant, did not even know there was a lead issue until she got an alert on her cellphone about the filter giveaway.

“Whoa, there’s lead in the water?” Ms. Grant remembered thinking.

Her mind flashed to her 7-month-old son, and she immediately called her husband. “I said, ‘Get more bottled water because we’re not giving the baby any more from the house.’”

No amount of lead exposure is known to be safe for children, whose mental and physical development can be impaired, according to the Centers for Disease Control and Prevention. In adults, lead can increase risks of high blood pressure and kidney disease; it can cause complications, including miscarriage, for pregnant women.

In Newark, about a quarter of the more than 14,000 children under 6 who were tested in 2016 had measurable levels of lead in their blood, according to an analysis by Advocates for Children of New Jersey of the most recent publicly available state data.

“This suggests a pervasive problem throughout the city coming from a variety of sources, and water could easily be one of them,” said Peter Chen, policy counsel at A.C.N.J.