"The good news is everyone is working together to make sure everyone stays calm," Schools Chancellor Joel Klein said.
But Nukeesha Swinnie, a public school parent and a graduate of the school whose assistant principal, Mitchell Wiener, died Sunday, said the city was not doing enough to slow the spread of the virus.
"They should close all the schools," a tearful Swinnie said at the makeshift memorial to Wiener at Intermediate School 238. "Don't wait for it to start."
The city Health Department said four Queens schools in three buildings were closing for up to five school days starting Tuesday. Earlier Monday, a private Catholic boys' school in Manhattan, St. David's School, decided on its own to close.
The latest closings come on top of Sunday's announced closing of four public schools and a Catholic school, bringing the total to 16 schools.
Hospital and city officials say complications besides the virus probably played a part in Wiener's death, but his family has said he suffered only from gout, a joint disease.
Autopsy results were awaiting further tests, said Ellen Borakove, a spokeswoman for the medical examiner's office.
Funeral arrangements hadn't been announced Monday, and Wiener's son Adam asked a reporter Monday to respect the family's wish to grieve privately.
Wiener's death was the sixth swine-flu-related fatality in the U.S.; officials have also reported three in Texas, one in Washington state and one in Arizona.
Wiener had taught in New York City for decades, starting as a substitute teacher in 1978. Since 2007, he had been an assistant principal at I.S. 238, also known as the Susan B. Anthony Intermediate School, in the Hollis neighborhood of Queens.
Swinnie said she attended the school, as did two of her children. She said one son, now 17, was "a rough kid" but Wiener took him in hand and made sure he passed.
"Mr. Wiener took a lot of time with him," she said. "He calmed him down."
As of Monday the swine flu virus has sickened more than 8,800 people in 40 countries, including more than 70 deaths.
The school closures in New York City affected more than 14,000 students. New York has the nation's largest public school system, with 1.1 million students. All but two of the closed schools are public.
No one else in the city besides Wiener has become seriously ill from the virus. Most people sickened from swine flu, or the H1N1 virus, have complained of mild, seasonal flu-like symptoms such as fever, cough, sore throat, body aches and fatigue.
The city health department said it is monitoring unusual clusters of flu cases as it works to stop the spread of the virus. Officials hope the school closures will help slow the spread of the virus "within the individual school communities," Health Commissioner Thomas Frieden said.
Assistant Principal Remembered As "Iron Man"
A day after Wiener's death, CBS News correspondent Bianca Solorzano reported that a message had been scrawled on the door of the school where Weiner had worked since 1978: "Rest in peace, Mr. Wiener."
Liz Leder, who worked at the same Queens school as Wiener, said her school's students share a bus line with student from St. Francis Prep, where the H1N1 flue was first spotted. "We have 1,600 kids, close to, in our building, so there's close proximity," she told Early Show anchor Harry Smith.
Leder said teachers and school officials were outraged at a lack of response after the St. Francis Prep outbreak. "We were paying attention. The principal was aware of it, Mitch Wiener was on top of it. They were making phone calls, they were talking to city agencies, you know, whoever they needed to contact. And it just seemed that whatever they were trying to do, no one was giving them any answers."
When asked about Weiner's reputation as an "iron man" who never got sick, she told Smith, "It was a joke around the building if he wasn't there, like, something seriously had to be wrong if Mitch didn't show up, because he just lived and breathed for I.S. 238. He'd been there over 30 years, assistant principal for about 20 of those years. He hired me when I first started."
She said the impact of the outbreak and the loss of Weiner hasn't sunk in yet for many of his co-workers. "I think everyone's in shock," Leder said.
Most people sickened from the H1N1 virus have complained of mild, seasonal flu-like symptoms. A hospital spokesman said complications other than the virus could have contributed to Wiener's death.
But Wiener's family insists he was only being treated for gout.
His wife, Bonnie Wiener, lashed out last week at city officials for not closing the school, when students were first diagnosed with swine flu.
"They can close because of snow, but not because of an illness that can be potentially deadly?" she told CBS Station WCBS.
WHO Annual Meeting Dominated By Swine Flu
In Geneva the World health organization will consider whether to raise its pandemic alert level to phase six. They will also discuss the H1N1 vaccine, with focus being placed on the Southern Hemisphere, where the flu season is about to begin.
Chile was the latest country Sunday to confirm a case of swine flu.
CBS News medical correspondent Dr. Jennifer Ashton said raising the alert level would mean an increase in mobilization of resources - including the production of flu shots.
The five-day meeting in Geneva, which involves health officials from the agency's 193 member states, will focus on fighting the swine flu outbreak and efforts to produce a vaccine.
WHO Director-General Dr. Margaret Chan will give experts' recommendations on which companies should produce a vaccine, how much they should make and how it could best be distributed.
The issue of producing a vaccine is sensitive, particularly for southern hemisphere countries where the annual flu season is about to begin. Seasonal flu can claim as many as 500,000 lives a year globally. But to have enough vaccine to confront a pandemic from a new strain such as swine flu, companies would switch production from vaccine production for seasonal flu.
WHO estimates up to 2 billion doses of swine flu vaccine could be produced yearly, though the first batches would not be available for four to six months.
Japan's Health Ministry confirmed dozens of new cases Sunday, prompting the government to close schools and cancel events such as Kobe's annual festival. By Monday, Japan's tally rose from five confirmed cases to more than 120.
Most of the new cases involved high school students in the western prefectures of Hyogo and Osaka who had not traveled overseas. Health officials said they were recovering in local hospitals or at home.
WHO spokesman Gregory Hartl said in-country transmission rates were a key factor in whether the global body decides to increase its pandemic alert level. Right now, the world is at phase 5 - out of a possible 6 - meaning a global outbreak is "imminent."
"We already know about the U.K. and Spain, that they have a relatively high number of cases compared to other European countries. So by simple virtue of the fact that they have more cases they need to be kept an eye on," Hartl said in an interview Sunday with AP Television News.
"There seems to have been activity in the last few days in Japan so we need to watch that, too," he said.
Spain and Britain have had the highest numbers of cases in Europe, reporting 103 and 101 cases, respectively. Britain on Sunday announced 14 new cases - 11 of them transmitted within the country.
A pandemic could be triggered if the virus starts to be transmitted from person to person on a large scale outside the Americas, WHO experts have said. But it would have to jump among people outside schools, hospitals and other institutions that typically pass on such viruses quickly.
"We don't want to prejudge anything, but certainly this is something we are watching with interest," Hartl said of the weekend developments in Japan.
U.N. Secretary-General Ban Ki-moon will visit WHO on Tuesday to meet with senior representatives from the vaccine industry, but the U.N. declined to name the companies.
WHO's health assembly will run through May 22, five days shorter than initially planned because health ministries are busy fighting the swine flu outbreak.
Taiwan received an observer seat on the World Health Assembly and is taking part for the first time in 38 years.