Lou Patch, a border patrol agent in El Paso, Texas, from where the shots were fired, confirmed that at least one agent opened fire during the Monday incident and said an FBI-led investigation was under way.
'Assaulted with rocks'
Patch told the AFP news agency that agents were "performing bike patrol duties" on a bridge linking the two countries when they were "assaulted with rocks by an unknown number of people".
"During the assault at least one agent discharged his firearm," he said.
The agent was placed on administrative leave and "a thorough multi-agency investigation is ongoing", he added.
The US state department said US agents responded to "a group of suspected illegal immigrants from Mexico".
"The agents were reportedly assaulted with rocks by an unknown number of people. During the assault, an agent discharged his firearm, killing one of the suspects. We regret the loss of life," the department said.
Mexican officials said that according to witness statements, the US agents on bicycle pursued the youths towards Mexico and that two of them opened fire.
Mexican state police had earlier provided a different version of events, saying the boy had been playing with two other youths on the Puente Negro bridge spanning the Rio Grande, linking Ciudad Juarez to El Paso.
Ciudad Juarez's attorney-general's office also said the youths were playing when they strayed into US territory inadvertently, and ran back towards the Mexican side after being surprised by the US agents.
The victim's parents said their son was killed inside Mexico and that he had no intention of crossing the border.
Jesus Hernandez, the father, told W Radio that his son went to the bridge to have lunch with his brother, who works nearby. At one point, "he went to the river bank to look to the other side".
"There were lots of kids and the border patrol cop ... started firing off shots and hit my son, my baby, twice in the head."
The teenager's death comes on the heels of a US investigation into the beating death last week of Hernandez Rojas, a 42-year-old Mexican father of five in US border patrol custody in San Diego, California, for deportation for crossing the border illegally.
Mexico's foreign ministry said the cases of Mexicans killed or injured in incidents involving use of force by US authorities have risen, "from five in 2008 to 12 in 2009 and 17 so far this year".
The increasing frequency of such incidents "reflects a disturbing increase in the use of excessive force by some authorities in the border area" the ministry said.
Roughly half a million people attempt to cross the 3,200km border from Mexico into the US each year, according to official figures.
Tensions have increased in recent months after the US-state of Arizona passed an anti-illegal immigration law which gives authorities powers to detain people on suspicion of being in the country illegally. The law has been criticised for infringing upon immigrants' rights.