Last week Mexico ordered the closure of restaurants, other businesses and tourist sites in an attempt to control the outbreak.
Hospitality sector representatives had said that the temporary closures were costing Mexico's economy $100m a day and threatening 450,000 jobs.
Need to 'over-prepare'
Twenty-six confirmed in Mexico, one in the United States
Countries with confirmed cases: Mexico, the US, Canada, Colombia, Costa Rica, El Salvador, China, South Korea, New Zealand, Israel, Spain, Britain, Germany, Austria, Switzerland, Denmark, France, Italy, Ireland, the Netherlands, Portugal
Countries with suspected cases: Australia, Brazil, Chile, Norway, Guatemala, India
Annual influenza epidemics are thought to result in three to five million cases of severe illness and between 250,000 and 500,000 deaths around the world, WHO says
The move to reopen businesses and schools comes as the number of cases of H1N1 flu confirmed by the World Health Organisation (WHO) passed the 1,000 mark.
Margaret Chan, the WHO chief, told the UN General Assembly in New York on Monday that the health body has recorded 1,003 cases of the influenza from across the globe.
Chan, however, said there was "no indication that we are facing a situation similar to that in 1918," when a flu pandemic killed about 50 million people.
But in comments published in a newspaper earlier on Monday, Chan warned that a second wave of the H1N1 virus "would be the biggest of all outbreaks the world has faced in the 21st century."
"I'm not predicting the pandemic will blow up, but if I miss it and we don't prepare, I fail. I'd rather over-prepare than not prepare," she told the Financial Times newspaper.
The WHO's global alert currently stands at phase five - signalling that a pandemic is imminent - while phase six would mean a pandemic, or global spread, was taking place.
Meanwhile, Portugal on Monday confirmed its first case of the new H1N1 strain, after a woman who had recently travelled back from Mexico tested positive for the virus.
Spain's health ministry also said on Monday that the number of confirmed cases in the country has risen to 54, from 44 a day earlier, but only 11 victims are in hospital.
Britain has also announced nine new H1N1 cases, taking to 27 the total number of people found to have the virus in the country.
At present 27 people have died from the H1N1 virus, which has affected 21 countries, according to the WHO.
One death was in the United States and the rest in Mexico.
US health authorities said more than half the nation's states had reported cases of the flu with 226 confirmed infections in 30 states.
Mexico China anger
In other moves Mexican diplomats complained to China on Monday after dozens of Mexican citizens were placed in quarantine despite showing no signs of having flu.
China's move came after a Mexican woman who arrived on a flight from Mexico was found to be suffering from the virus.
Ma Zhaoxu, a spokesman for the Chinese foreign ministry, said the isolation was correct procedure and was not an act of discrimination against Mexicans.
Mexican officials said they were preparing to send a specially chartered aircraft to China to pick up any Mexicans who wish to return.