Restaurants and cafes in Mexico City are to reopen on Wednesday after the country recorded a fall in new cases of the swine flu virus.
Libraries, museums and churches are to follow suit a day later but cinemas, theatres and bars are to remain closed, the mayor's office said.
Government officials are meeting to discuss when schools and businesses across the country can resume work.
A total of 1,025 cases of the virus have been reported in 20 countries, BBC reported.
Confirmed cases in the US have risen from 226 to 286, spread over 36 states, with most patients suffering mild symptoms. One death has been confirmed - that of a Mexican two-year-old boy who was visiting Texas.
Officials say the rise in cases in recent days was due to results of lab tests coming through, rather than because of a new surge in cases.
The UN says it has seen no evidence of a spread at community level in Europe and Asia - a development that would trigger the highest level of alert.
Dr Keiji Fukuda, deputy chief of the World Health Organization (WHO), told reporters it was essential that surveillance remained strong worldwide.
Surveillance has to be strong everywhere, Dr Fukuda said.
"Right now we really just don't know how this will go."
Secondary transmission, ie to persons who have not visited Mexico, has been confirmed in six countries.
The virus is suspected of claiming 101 lives in Mexico though the number of confirmed cases there is 26, its health minister said on Monday.
Of nine new confirmed cases of swine flu in the UK, seven appear to have been acquired from people who had not been to Mexico; total confirmed cases stood at 27.
About 250 recruits and personnel at an army camp in the western Swiss canton of Fribourg were placed under quarantine after two recruits reported having flu symptoms.
Mexico's shutdown is credited with stemming the spread of the virus but it badly affected the country's economy.
President Felipe Calderon went on national TV on Sunday night to say a nationwide shutdown and an aggressive information campaign appeared to have helped curtail the outbreak in Mexico.
"We have succeeded in detaining or at least slowing the spread of the virus precisely because the measures have been the correct ones," he said.
Swine flu has been confirmed as the cause of 26 deaths in Mexico and 701 people have been infected, Health Minister Jose Angel Cordova said on Monday.
Earlier, he had said the epidemic was "in its phase of decline", having peaked between 23 and 28 April.
Ban Ki-moon called for global co-ordination on swine flu
Talking about the possible reopening of schools, he warned it would "not happen just like that". "There will have to be training, preparations for teachers and parents," he told reporters.
Inhabitants of the capital interviewed by Reuters news agency on Sunday spoke of their frustration at the upset caused by the restrictions.
"They should open everything back up so we can work," said Alberto Vazquez, 28, who washes cars for a living.
"These last days have been hard on us. If we don't work, we don't eat."
Mexico has criticised China for placing in quarantine up to 70 Mexicans, even though they showed no sign of having contracted swine flu.
It said it was sending a plane to Beijing to pick up the Mexicans as China denied it was being discriminatory.
A Mexican man staying in a Hong Kong hotel was confirmed to have contracted the virus on Friday. More than 250 guests and staff at the hotel are being held under quarantine for a week.
WHO chief Margaret Chan sought to ease concern that swine flu, or H1N1, might develop into a pandemic similar to the Spanish Flu which killed tens of millions at the end of World War I.
"[There is] no indication that we are facing a situation similar to that in 1918," she told a meeting of the UN General Assembly in New York, speaking by video link from Geneva.
But she also cautioned against complacency: "Flu viruses are very unpredictable, very deceptive... We should not be over-confident. One must not give H1N1 the opportunity to mix with other viruses."
UN chief Ban Ki-moon, in New York, said the WHO did not plan to raise its pandemic alert to the highest level if the outbreak continued in its current pattern.
The severity of the swine flu virus remains uncertain, the BBC's Imogen Foulkes reports from Geneva.
Health experts worldwide want to know which population groups are most vulnerable and why the virus has caused severe pneumonia among some patients, and diarrhoea - not normally associated with flu - in others, our correspondent says.
On Tuesday the WHO will hold a meeting of doctors and scientists to discuss these questions. The answers, the WHO says, will help all those working to control and treat the virus.