Some parents say it's too soon to send the children back to the classrooms.
Two schools that reopened last Friday saw barely half of their students return to class.
Another 17 schools are set to reopen on Thursday.
Meanwhile, a woman died over the weekend of swine flu, becoming the city's second victim and the nation's 11th.
Then, on Monday, a Chicago resident died of swine flu. That person was the first death in Illinois and the 12th nationally from the illness, according to health authorities.
Authorities in Mexico, where the swine flu outbreak was identified in April, announced three more deaths, raising its total to 83, and Canada reported its second death.
"With as many cases of H1N1 influenza that have been reported in Illinois, we have been concerned that there would be fatalities," said Dr. Damon Arnold, director of the Illinois Department of Public Health. The state lists 896 confirmed cases of the illness, known both as H1N1 and swine flu.
Before the latest reports, the World Health Organization tallied at least 91 deaths around the globe from more than 12,500 swine flu cases. The Centers for Disease Control and Prevention counted 10 deaths and 6,700 cases in the U.S., most of them mild. New York health officials reported another death over the weekend.
At least 46 countries have confirmed cases, according to WHO.
Puerto Rico reported its first case Monday, making it the second Caribbean island to confirm the illness. The man is recuperating at home.
The New York City fatality, a woman in her 50s and lived in Queens, had other health conditions, Department of Health and Mental Hygiene spokeswoman Jessica Scaperotti said. No other information on her case was disclosed Sunday.
Assistant public school principal Mitchell Wiener, who died May 17, was the city's first death from the virus. The 55-year-old had been sick for several days.
For facts about influenza, and more information about swine flu, please visit the Health Department and CDC websites. Some specific resources:
From New York City Health Department
Facts about flu
From Centers for Disease Control and Prevention
General information about swine flu
Swine Flu Case Definitions
Swine Flu Infection Control and Patient Care
Preventing the Flu