But countries advised not to close borders
Companies across the world are restricting travel as the World Health Organization (WHO) raises its swine flu alert to just two short of a full pandemic.
Dr Keiji Fukuda, a flu expert with the WHO, said containment was not "a feasible operation" as the infection had already spread "quite far."
But Dr Fukuda said told a press conference the WHO was not recommending that countries close their borders or impose travel restrictions.
"Given the current situation, the current focus of efforts should really be on mitigation efforts rather than trying to contain the spread virus, predominantly because this virus has already spread quite far," he said.
"The [WHO] director general recommends not closing border or restricting travel. However it is prudent for people who are sick to delay travel."
The UK Foreign and Commonwealth Office (FCO) today (April 28) revised its travel advice in response to the WHO announcement.
"We are now advising against all but essential travel to Mexico," the FCO said.
The WHO's pandemic threat level now stands at four for "evidence of increased human to human transmission".
While companies are reported to be stepping up precautions, none are yet known to be imposing all out travel bans.
Airports in Asia, Latin America and Europe have begun screening inbound passengers for symptoms, the BBC reported today.
Germany's largest tour operator has also suspended trips to Mexico, reports said.
Androulla Vassiliou, EC health commissioner, yesterday warned people not to travel to parts of Mexico and the US hit by the outbreak in swine flu.
Two cases of the deadly disease have so far been confirmed in the UK, with further known or suspected in countries including the US, Canada, Spain and New Zealand.
"There have been a total of 149 deaths of which twenty have been confirmed as linked to the new variant influenza," the FCO said.
"Most cases have been reported in Mexico City, together with a number of other locations across the country."