Xavier Zamora, 17, of Albuquerque, Jose Hernandez on Monday afternoon.
Zamora in a dispute with Zamora's mother outside her house, and decided to help her to escape the fight, Albuquerque police say.
Hernandez sprayed Mace on Zamora when she became angry with him.
Hernandez in the abdomen before going back inside, according to police.
Someone tried to resuscitate Hernandez, but the 47-year-old mail carrier and Army veteran eventually died of his wound, police say.
Police were called, and SWAT officers surrounded the house. Zamora had fled, police said.
Zamora is 6 feet tall, has brown hair and brown eyes, and weighs 165 pounds, according to a warrant issued for his arrest.
Everyone in the neighborhood knew the mail carrier, a resident says
"Jose was a very special guy – he was not your ordinary mailman," Michael Shepherd told KOAT. "He'd go out of his way." He would talk to you. "
By Tuesday, people had left flowers and notes outside the house in Hernandez's memory, KOAT reported.
One of the best wishes of the letter is "To a great mail carrier who sacrificed his life for the greater good." "We want all remember you."
Hernandez, a carrier from the city's Five Points post office, worked for the US Postal Service for 12 years, the agency said.
Postal Service spokesman Rod Spurgeon said "We are shocked and saddened to learn of a tragic death of one of our own employees and coworkers." Army veteran.
The Postal Service is offering assistance to his family and coworkers. "
The shooting has shaken the city, Mayor Tim Keller said.
"We are grieving with the family of the victim, and with the entire postal service family," Keller said. "Fighting crime wants to remain our top priority."
"Albuquerque, please take some time in the next few days to make sure your local letter carrier knows how much you appreciate them, and give them your love and support."
CNN's Amanda Watts and Casey Hicks contributed to this report.