He was a nephew of Pedro Menéndez de Avilés, who had been appointed adelantado (an elite military and administrative position) of La Florida by King Philip II.
As Pedro Menéndez de Avilés was preparing his expedition to found a colony in Florida, he appointed Márquez as second-in-command of the fleet sailing from Asturias.
After the founding of St. Augustine and the expulsion of the French from Fort Caroline, Márquez was dispatched to carry the official report to Spain, in command of the ships returning there for supplies.
[1][12] In October 1577, Márquez replaced Hernando de Miranda as governor of Santa Elena, located on what is now called Parris Island in Port Royal Sound, and reoccupied the settlement with a military force under his command.
Márquez, anticipating that the Indians might attack any Spaniards who tried to return to Santa Elena, brought a prefabricated fort from St. Augustine and with 53 men erected it in just six days.
[15] Márquez ordered his soldiers to build a new wooden fort to defend the city, and brought the settlers of the failed colony to the capital of La Florida.