President Barack Obama urged calm, saying there was reason for concern but not yet "a cause for alarm."
Yet just in case, administration officials said that they were already waging a vigorous campaign of prevention, unsure of the outbreak's severity or where it would show up next.
U.S. customs officials began checking people entering U.S. territory. Millions of doses of flu-fighting medications from a federal stockpile were on their way to states, with priority given to the five already affected and to border states. Federal agencies were conferring with state and international governments.
"We want to make sure that we have equipment where it needs to be, people where they need to be and, most important, information shared at all levels," Janet Napolitano, head of the Homeland Security Department, told reporters.
Her briefing came shortly before the World Health Organization raised the severity of its pandemic alert level to four from three on a six-point scale. Level four means there is sustained human-to-human spread in at least one country. Level six is a full-fledged pandemic, an epidemic that has spread to a wide geographic area.
"We are proceeding as if we are preparatory to a full pandemic," Napolitano said.
She said travel warnings for trips to Mexico would remain in place as long as swine flu is detected.
Dr. Richard Besser, acting director of the Centers for Disease Control and Prevention, said that so far the disease in the United States seemed less severe than the outbreak in Mexico, where more than 1,600 cases had been reported and where the suspected death toll had climbed to 149. No deaths had been reported in the U.S, and only one hospitalization.
"I wouldn't be overly reassured by that," Besser told reporters at CDC's headquarters in Atlanta. He raised the possibility of more severe cases - and deaths - in the United States.
A European Union official warned against travel to parts of the U.S. as well as Mexico, but Besser said that seemed unwarranted.
State Department spokesman Robert A. Wood said the EU commissioner's remarks were his "personal opinion," not an official position, and thus the department had no comment. "We don't want people to panic at this point," Wood said.
Still Besser said of the situation, "We are taking it seriously and acting aggressively. ... Until the outbreak has progressed, you really don't know what it's going to do."
The U.S. stepped up checks of people entering the country by air, land and sea and issued a new U.S. travel advisory suggesting "nonessential travel to Mexico be avoided."
As the number of cases continues to climb, Mexican and American health officials are urgently trying to zero in on the origins of the outbreak. One potential lead, reports CBS News correspondent Hari Sreenivasan is the massive industrial hog farms that have sprung up in Mexico in recent years - some operated by U.S. companies such as Virginia-based Smithfield Foods.
They deny being the source and say they're cooperating with health officials. But Sreenivasan reports that just last year, a report by the nonprofit Pew Charitable Trusts warned that hog farms could become breeding grounds for new strains of the flu.
"The warm conditions and the close proximity of animals being able to pass viruses back and forth and to the human workers," said Bob Martin of the Pew Environmental Group. "It's a situation ripe for the development of a novel virus."
The confirmed cases announced on Monday were double the 20 earlier reported by the CDC. Besser said this was due to further testing - not further spreading of the virus - in New York at St. Francis Prep School in Queens, bringing the New York total to 28.
CBS News' Ryan Corsaro and Chris St. Peter have learned that employees at a top accounting firm in New York City, Ernst & Young, were notified Monday that a . An e-mail was sent notifying staff that the employee became ill after contact with a family member who was exposed to the virus, and is now doing well.
Monday evening, New Jersey health officials said they have identified five probable cases of swine flu in people who recently traveled to Mexico and California.
The New Jersey Department of Health and Senior Services said Monday that all have mild forms of the flu and none has been hospitalized. The department is arranging for confirmatory testing at the CDC.
Also, 14 schools in Texas, including a high school where two cases were confirmed, will be closed for at least the next week. Some schools in California and Ohio also were closing after students were found or suspected to have the flu.
The CDC is releasing 11 million doses of the stockpiled anti-viral drug Tamiflu to affected areas, reports CBS News correspondent Kelly Wallace. New York City pharmacists report a run on the drug, which requires a doctor's prescription. But the CDC fears that doctors giving it to patients who don't really need it may cause shortages for those who are sick.
Ariana Drauch, a swine flu victim from St. Francis Prep, told Wallace her family can't find it anywhere.
"We called every drug store in Queens, New York, everywhere," Drauch said. "And there is no Tamiflu available."
Besser said other cases have been reported in Ohio, Kansas, Texas and California. He said that, of the 40 cases, only one person has been hospitalized and all have recovered.
Countries across the globe increased their vigilance amid increasing worries about a worldwide pandemic. Obama told a gathering of scientists that his administration's Department of Health and Human Services had declared a public health emergency "as a precautionary tool to ensure that we have the resources we need at our disposal to respond quickly and effectively."
"This is obviously a cause for concern and requires a heightened state of alert, but it's not a cause for alarm," Obama said. He said he was getting regular updates.
The Senate has yet to confirm a secretary of human services, a surgeon general or a director of CDC. The absence of those officials left Besser and Napolitano to brief reporters on the swine flu outbreak.
The quickening pace of developments in the United States in response to the spreading new flu strain was accompanied by a host of varying responses around the world.
Mexico, at the center of the outbreak as the from the disease, suspended schools nationwide. China, Taiwan and Russia considered quarantines, and several Asian countries scrutinized visitors arriving at their airports.
U.S. customs officials began checking people entering U.S. territory. Officials say there is a program of passive surveillance for every one of the 600,000 people who enter the United States from Mexico every day, reports CBS News correspondent Dean Reynolds from the border at El Paso, Texas. Under the program visitors displaying symptoms would be questioned and isolated if need be.
"The traveling public probably won't notice much difference in our inspectional procedures but the officers have been briefed on the actions to take if they encounter someone who appears ill," said Roger Maier of the U.S. Customs and Border Protection.
If a traveler reports not feeling well, the person will be questioned about symptoms and, if necessary, referred to a CDC official for additional screening. The customs officials were wearing personal protective gear, such as gloves and masks.
The CDC can send someone to the hospital if they suspect a case, but no one is being refused entry. Also, the CDC is readying "yellow cards" with disease information for travelers, in case they later experience symptoms. The border monitoring resembles that done during the SARS epidemic earlier in the decade.
Multiple airlines, including American, United, Continental, US Airways, Mexicana and Air Canada, said they were waiving usual penalties for changing reservations for anyone traveling to, from, or through Mexico, but had not canceled flights.
Napolitano urged Americans to take "common sense" precautions.
"Common sense means washing hands, staying home from work or school if you feel sick, covering your mouth if you cough or sneeze. These are straightforward and simple measures, but they can materially improve our chances of avoiding a full-fledged pandemic," she said.
Administration officials said about 11 million doses of flu-fighting medications from a federal stockpile have been sent to states in case they are needed - roughly one quarter of the doses in the stockpile.
While there presently is no vaccine available to prevent the specific strain now being seen, there are antiflu drugs that do work once someone is sick. If a new vaccine eventually is ordered, the CDC already has taken a key preliminary step - creating what's called seed stock of the virus that manufacturers would use.
Stock markets fell overseas and in the United States out of concern that the outbreak could derail economic recovery. Airline and other travel-related stocks suffered the sharpest losses.
Swine Flu News Worldwide: