"Columbine. Virginia Tech. Sandy Hook. Las Vegas. Orlando. Parkland," Cuomo wrote in the letter Friday, ticking off locations of recent mass shootings. "And now, Santa Fe."
"When is enough enough? How many more innocent people have to die before you act?" he added.
At least eight people, mostly students, died Friday after a student allegedly opened fire at Santa Fe High School, which is located between Houston and Galveston, Texas, authorities said. The investigation is ongoing.
The massacre comes just three months after 17 people were killed on Valentine's Day in a shooting at Marjory Stoneman Douglas High School in Parkland, Florida.
Trump called the Texas school shooting an "absolutely horrific attack." He told the victims and their families, "We're here with you in this tragic hour and we will be with you forever."
"We're closely monitoring the situation and federal authorities are coordinating with local officials. This has been going on for too long in this country, too many decades," the president said Friday during an event at the White House. "Everyone must work together at every level of government to keep our children safe."
In his open letter to Trump and members of Congress, Cuomo urged them to "do something" about gun violence.
"You were elected to lead -- do something," the Democratic governor wrote. "Your first responsibility is to the people of this country, not the NRA -- do something. My heart breaks for the families who have to grieve from this needless violence -- DO SOMETHING."