(Adds details on Sinaloa case)

MEXICO CITY, Feb 28 (Reuters) - Mexico's government said on Friday it had detected the first cases of coronavirus infection in two men who had recently traveled to Italy, making the country the second in Latin America to register the fast-spreading virus.

A 35-year-old man who showed positive in an initial test in Mexico City went through a second test that turned up positive results early on Friday, Deputy Health Minister Hugo Lopez-Gatell Ramirez told a regular news conference.

The man was linked to the second case, a 41-year-old in the northern state of Sinaloa, Lopez-Gatell told reporters, speaking alongside President Andres Manuel Lopez Obrador.

Lopez Obrador urged the population to remain calm.

"We have the capacity to handle this situation," he said. "Because according to the information available, this is not something terrible, really bad."

The government will hold a daily 9 p.m. news conference until further notice to update the public on the coronavirus infections, Lopez Obrador added.

Mexico's main stock index suffered one of its biggest falls in months, tumbling more than 4% in morning trading, while the peso fell by more than 1% against the dollar.

Both of the men confirmed with coronavirus were in Italy for about a week in mid-February, and likely became infected at a convention in the northern city of Bergamo, the government said.

The two were being held in isolation, one in a hospital and the other in a hotel in Sinaloa, Lopez-Gatell said.

The Mexico City resident had light, cold-like symptoms and was at low risk, he added. Officials were observing five of his family members in isolation.

The man in Sinaloa did not show symptoms, Sinaloa's health minister Efren Encinas said at a separate news conference.

Officials were checking the man's companion, who was also in isolation, and identifying passengers on the flight from Italy who may have had contact.

In addition, two men who had been in direct contact with the infected men were under observation, one in isolation, the government said.

For now, there are no grounds for closing schools or having people stay away from their workplaces, Lopez-Gatell said.

"There's absolutely no reason at this point," he added. "There is no generalized transmission."

Still, Lopez-Gatell recommended that people refrain from light hugs and kisses on the cheek that are commonplace greetings in Mexico.

Previously, Brazil had been the only country in Latin America to report a case of the new coronavirus. (Reporting by Daina Beth Solomon, Lizbeth Diaz and Raul Cortes Fernandez; Editing by Nick Zieminski, Steve Orlofsky and Dan Grebler)

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