Fidel Castro, meanwhile, accused Mexico of hiding the epidemic until after President Barack Obama visited last month.
Mexican Health Secretary Jose Cordova said his nation's shutdown of schools - which was lifted in most of the country's 31 states Monday - had averted an avalanche of cases.
"It would have been difficult for us to have controlled this epidemic," Cordova said in a statement, adding that Mexico had 56 deaths and 2,059 confirmed cases of swine flu.
But Castro, the former Cuban president, accused Mexico of failing to disclose the spread of swine flu until after Obama had visited en route to the Summit of the Americas in Trinidad last month.
"Mexican authorities did not inform the world of the presence (of swine flu), while they waited for Obama's visit," he wrote on a government Web site hours after Cuba confirmed its first swine flu case.
Obama's April 16 visit came a week before Mexican health officials announced swine flu was spreading, prompting an eventual mass shutdown that brought many parts of the country to a virtual halt.
Thailand and Finland reported their first confirmed swine cases Tuesday of people just arrived from Mexico. Cuba and China - both countries that had imposed strict measures on flights and travelers from Mexico - also reported their first confirmed cases.
Cuba identified its patient as a Mexican student attending a Cuban medical school and China said its case involved a Chinese student who had just returned from the United States.
At least 61 people have been killed by swine flu around the world, and the World Health Organization has confirmed over 5,250 cases.
Cuba's Health Ministry said a group of medical students from Mexico began arriving on the island to resume their studies April 25 - four days before Cuban authorities halted airline flights from Mexico. Fourteen of the students suffered from flu-like symptoms.
A study published Monday in the journal Science estimated Mexico alone may have had 23,000 cases of swine flu by April 23, the day it announced the epidemic. The study estimates swine flu kills between 0.4 percent and 1.4 percent of its victims, but lead author Neil Ferguson of Imperial College, London, said the data remain incomplete.
"It's very difficult to quantify the human health impact at this stage," he said.
The analysis in Science suggests there are many more cases than those confirmed by laboratories - anywhere from 6,000 to 32,000 cases in Mexico as of April 23. The flu has since spread around the world, and the study said it appears to be substantially more contagious than normal, seasonal flu.
Researchers also compared the genetic sequences of the viruses in 23 confirmed cases, and came up with an estimate of Jan. 12 for their earliest common ancestor - presumably when person-to-person transmission began. But they said it could have been anywhere from Nov. 3 to March 2.
The researchers said the 2009 H1N1 flu appears to be about equal in severity to the flu of 1957 and less severe than the deadly 1918 version.
In Mexico, Monday's reopening of kindergartens and primary and middle schools shut since April 24 was the latest step in efforts to restore a sense of normality. Businesses, government services, high schools and universities reopened last week.
But six of Mexico's 31 states put off reopening schools for a week because of local rises in the number of flu cases, and a seventh pushed it back a day to Tuesday. The Education Department said it will tack an extra seven days onto the school calendar to make up for the lost time.
But while officials praised the health and education systems for their response to the crisis, there were signs that Mexico's overburdened health system was under strain.
Dozens of government health care workers, including doctors and nurses, marched and blocked streets in the Gulf coast city of Jalapa to demand higher pay and better working conditions.
"The government asked our help in combatting the influenza epidemic, now we are asking the government to do us justice," said nurse Mariana Cortes, one of the protest organizers.
Mexico is trying to revive its economy after the epidemic pummeled tourism, the country's third-largest source of legal foreign income. Mexico provided details Monday of a $1.1 billion package to help restaurants, hotels and other businesses.
At least 10 commercial banks are involved in the plan, promising three-month reprieves for small businesses with outstanding loans in Mexico City and two hard-hit states. Small businesses in beach resorts and other tourist destinations were promised a six-month grace period.
Later in the day, Tourism Secretary Rodolfo Elizondo said the government would launch a $90 million publicity campaign this week urging Mexicans to vacation at home.
Noting that several nations have issued travel warnings or restricted airline flights to Mexico, Elizondo said trying to promote trips to Mexico by foreigners now "would be like throwing money away."
With Cuba, Thailand and Finland reporting their first cases, the number of countries reporting confirmed swine flu cases grew to 33. The United States has the most confirmed cases - 2,618 - according to the U.S. Centers for Disease Control and Prevention. Swine flu has killed 56 people in Mexico, three in the U.S., one in Canada and one in Costa Rica.