To accomplish that, Martínez asked the state Motor Vehicles Division and Taxation and Revenue Department to begin an administrative effort to improve security in the system of issuing the licenses.
Martínez has put special emphasis on the regulations that demand foreigners verify their residence in the state.
The Republican governor said Wednesday in a communique that she hoped to receive recommendations and take action on the matter by the end of July.
Martínez has said she feels that the procedure whereby New Mexico issues driver's licenses is one of the "least secure" in the country due to a state law that allows undocumented immigrants to obtain the document.
In her opinion, this has attracted the attention of people who come to New Mexico from other states and even other countries with the sole intention of obtaining a driver's license.
In the communique, Martínez says that about 35 percent of the calls made to the MVD by people wanting to make an appointment to obtain a driver's license come from telephones outside the state.
At the end of May, at Martínez's request, the MVD stopped accepting notarized letters of residence as proof of residence in the state.
The governor is also seeking to establish a system to verify that all undocumented immigrants who have gotten driver's licenses in the state really live in New Mexico.