"Acapulco airport has already been reopened for an airlift," Defense Minister Luis Cresencio Sandoval told reporters in Mexico City, adding that the runway had not suffered major damage.
Commercial airlines would bring in doctors and fly out tourists and locals, he added.
Passengers hauling suitcases arrived at Acapulco International Airport to catch free flights, expressing relief to be alive after Hurricane Otis smashed into the city with winds of 165 miles (270 kilometers) per hour.
"We're very happy and content, grateful to be able to continue living our lives" said Clara Elena Albo from Mexico City, who was on vacation with her husband.
The airport buildings and installations appeared to be severely damaged, with broken glass and debris littering the ground.
The control tower and navigation systems were severely affected, so flights will be operated visually.
Lucina Ahuelican said that she had been stranded at the airport with her two daughters since Tuesday night.
"There was a lot of desperation... not knowing when we were going to leave," the 40-year-old said.
Some visitors left by road after the main highway to the capital was reopened.
- Pope offers prayers -
Once a magnet for Hollywood stars, Acapulco's fun-loving reputation has been tarnished by drug-related violence in recent years, though it remains a popular destination for Mexicans and some foreigners.
Hurricanes hit Mexico every year on both its Pacific and Atlantic coasts, usually between May and November, though few make landfall as a Category 5.
Otis partially destroyed many buildings, shattering windows and leaving gaping holes in the walls of high-rise towers.
Tourists have said they used beds and mattresses for protection in their hotel rooms.
Others took shelter in bathrooms.
Four people remained missing, including three members of the Navy, according to the government.
Pope Francis sent a message of condolences and prayers for "the eternal rest of the deceased," the Vatican said.
Before hitting land early Wednesday, Otis rapidly intensified within hours from a tropical storm to the most powerful category of the five-step Saffir-Simpson scale, taking authorities by surprise.
The World Meteorological Organization described the hurricane as "one of the most rapidly intensifying tropical cyclones on record."
Much of Acapulco remained without electricity or telephone connections on Friday, while food was scarce, leading to looting of supermarkets.
The government said that it had activated an emergency plan to bring in essential supplies.
Social media platforms were flooded with messages from people seeking news of their relatives.
The army provided some satellite phones for residents to communicate with family members.
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