President Enrique Pena Nieto welcomed the royal couple at the Campo Marte military field in Mexico City, where they were treated to a cannon salute and a military parade.
"This visit will serve to compare again the many things that 170 million Mexicans and Spaniards have in common, and the enormous potential in front of us," Felipe said.
The state visit went ahead as planned even though Pena Nieto underwent emergency surgery on Friday to remove his gall bladder after a sudden inflammation.
He was discharged from the hospital on Sunday.
After the military event, the royals were honored as "distinguished guests" of the capital during a visit to Mexico City's Mayor Miguel Angel Mancera.
At a state dinner on Monday evening Queen Letizia looked stunning in an off the shoulder red sequined dress.
Felipe traveled to the eastern port of Veracruz in December to attend the Ibero-American Summit, but this is his first state visit since ascending to the throne in June 2014.
Felipe will address Mexico's Senate on Tuesday. The next day, the king and queen will visit the northern state of Zacatecas for a cultural tour.