Cuomo also authorized the deployment of 115 National Guard member to Puerto Rico during the next 90 days to assist in emergency response efforts.
"The point of the visit is basically to assess the damage and determine how we can best help," Cuomo said. "Can we help with engineering? Can we help with the power plant? Can we help with supplies? What do they need that we can best provide?"
The ground in southwest Puerto Rico has been shaking since Dec. 28, with more than 1,280 earthquakes, of which more than 100 were felt and more than 70 were of magnitude 3.5 or greater. Recent quakes have toppled homes and schools.
Cuomo started his visit Tuesday with a helicopter ride to get a birds-eye view of the damage before he hit the ground running in Ponce and Guanica.
Ponce is the island's second largest city and a power plant there sustained significant damage. Meanwhile destruction could be seen around nearly every corner in Guanica.
Residents are staying in shelters in Ponce because they are too afraid to stay in their own homes, and that's a fear that Cuomo understands.
"They're not making an irrational decision, members of my team who have been here for a few days who were staying in a hotel felt the tremors, got out of the hotel, and slept in a car because it's frightening," Cuomo said. "Some of these homes have some damage and you see a crack and you don't know if that crack is structural or if there's another tremor, if it's going to be a real problem. So it's a logical response and our responsibility on a number of levels is to get a large number of inspectors here to look at these homes so people can be sure the home is safe to sleep in."
The director of Puerto Rico's Electric Power Authority has ordered the temporary closure of the company's largest plant, which crews had been inspecting for damage caused by earlier quakes.
Cuomo directed the New York Power Authority to assist in recovery efforts last week alongside the Puerto Rican Electric Power Authority. The NYPA has deployed multiple teams of power grid experts to Puerto Rico since Hurricane Maria in 2017.
"Puerto Rico is still hurting from the destruction caused by Hurricane Maria and the federal government's protracted recovery over two years ago, and now the island is once again being dealt a devastating blow with a series of earthquakes and tremors that has caused widespread damage and power outages, leaving thousands of families in shelters," Cuomo said. "From day one New York has been a tremendous supporter of the recovery efforts in Puerto Rico, and we will continue to stand shoulder to shoulder with the island during these challenging times. New York State will deploy National Guard to assist in emergency response efforts, and I will be traveling with a delegation to assess the damage and determine what more we can do to help."
Cuomo and the National Guard members are joined by Bronx Borough President Ruben Diaz, Jr. and State Assemblyman Marcos Crespo.
"My family has been affected by this," Crespo said. "My friends and neighbors have been affected by this. My people have been affected by this."
Mental health experts also traveled to the island from New York to help with anguish and anxiety suffered by so many people who have not spent time in their homes for weeks.
Many people who have abandoned their homes now seek safety in tent cities, including Orlando Alvarado, who is one of 14 members living in a tent city in Ponce. He says at night, more people continue to arrive simply to escape the potential danger of a building collapse.
The flurry of earthquakes topped by a magnitude 6.4 temblor that killed one person and damaged hundreds of buildings has many accusing the Puerto Rico government of being caught unready again.
"They need blankets, they need cots, they need tents, they need sleeping bags," Diaz said. "People are sleeping outside in the elements because they fear if they sleep indoors, even if their homes are not compromised, at some point it may fall on their heads."
WABC reporter Joe Torres says he has noticed a tremendous show of solidarity among the people of Puerto Rico who have come from every corner of the island to help their brothers and sisters.
"No matter what happens, we all could be in the same situation," relief worker Ivette Cruz said. "We always stick together."
Meanwhile, New York City Mayor Bill de Blasio announced plans to send 24 more City personnel to Puerto Rico to assist with the recovery.
-- The Associated Press contributed to this report.