The US declared a public health emergency on Sunday, after confirming 20 cases of swine flu across five states.
The World Health Organisation (WHO) has warned that the new H1N1 swine flu virus - apparently a mix of human, pig and bird viruses - could become a pandemic.
New Zealand has also reported that 10 students who had travelled to Mexico had tested positive for influenza and were "likely" to have contracted swine flu.
Suspected cases are also being investigated in the Middle East and elsewhere in Asia.
In the US, Richard Besser, the acting head of the Centres for Disease Control (CDC), told a White House press conference that there were eight confirmed cases of swine flu in New York City, seven in California, two in Texas, two in Kansas and one in Ohio.
"As we look for cases of swine flu, we are seeing more cases of swine flu. We expect to see more cases of swine flu," he said.
"We're responding aggressively to try and learn more about this outbreak."
Janet Napolitano, the US homeland security secretary, said that the emergency declaration was "standard operating procedure".
She said the declaration "allows us to use medication and diagnostic tests that we might not otherwise be able to use, particularly on very young children, and it releases funds for the acquisitions of additional anti-virals".
"All persons entering the United States from a location of human infection of swine flu will be processed through all appropriate CDC protocols," she added.
Mexico has already issued an emergency decree, giving the government the powers to isolate sick people, enter homes or workplaces and regulate air, sea and land transportation to try to stop further infection.
Margaret Chan, the WHO chief, warned on Saturday that the "virus has clearly a pandemic potential".
Later, Keiji Fukuda, acting WHO assistant-general for health, security and the environment, said the virus could mutate into a "more dangerous strain".
Severe Acute Respiratory Syndrome, or SARS, first reported in Asia in February 2003 and spreads to 29 countries before being contained in May 2004.
The World Health Organisation says Sars killed 774 people and sickened 8,098 others.
First human infections with H5N1 virus, or 'bird flu', reported in Hong Kong in 1997. Six out of 18 cases prove fatal.
By 2009, 257 deaths from bird flu are recorded worldwide, with Indonesia the worst hit. Seven people in China and Vietnam die.
Ebola Reston virus found in pigs and six humans in the Philippines in 2009 in what is believed to be the virus' first transmission from pigs to humans.
But Fukuda said that if there is such an escalation, the world is better prepared now than it has been in the past.
Following the outbreak of Severe Acute Respiratory Syndrome (Sars) in 2003, which killed nearly 800 people, and amid regular reported bird flu cases, countries have stepped up preparations against a pandemic.
This include national strategies to deal with any outbreak, as well as stockpiles of anti-viral drugs.
The WHO itself holds a stockpile of about five million treatment courses of the anti-viral drug Tamiflu, Fukuda told journalists.
Dr John Simon, a consultant in infectious diseases and tropical medicine in Hong Kong, told Al Jazeera that anti-viral drugs could be used to combat the virus.
"It is an H1N1 virus and that is easy to treat with anti-viral drugs - I am not saying it is going to be easily containable, but it should be quite responsive to treatment," he said.