The three victims died in drive-by shootings in two separate attacks
American FBI agents have been sent to the Mexican border city of Ciudad Juarez to investigate the deaths of three US citizens.
Three people connected to the consulate were killed in drive-by shootings on Saturday in two separate incidents.
The US state department said the killings underscored the "severe and significant danger" drug gangs represented to Mexico and the US.
Mexico has blamed the killings on a gang linked to a drugs cartel.
But investigators have said it is too early to tell if those killed were deliberately targeted.
"It could be a mistaken identity, it could be that they were targeted; we don't know at this point," special agent Andrea Simmons, a spokesman for the FBI's El Paso, Texas, office told Agence France-Presse.
Some eight FBI agents will be working alongside Mexican authorities in the investigation, she added.
On Saturday, Lesley Enriquez - a US citizen working at the Juarez consulate - her American husband, Arthur Redelfs, and Jorge Alberto Salcido - the Mexican husband of another consular employee - were shot dead in two separate incidents.
Both couples had just left a social event in the city when they were killed.
Enriquez, 35, and her 34-year-old husband were killed in a hail of bullets as they drove their car towards the US side of the border. Their one-year-old baby was found unharmed in the back seat.
In the second attack, gunmen opened fire on the car belonging to Jorge Alberto Salcido, killing him and wounding his two children.
The state department said the killings were a "tragedy".
"We all share the determination that, ultimately, through a variety of means, we will take back these streets one community at a time," state spokesman PJ Crowley told a news briefing.
"The tragedy of this weekend just underscores how severe and significant a danger this represents to Mexico, to the United States, to the hemisphere."
His comments come a day ahead of a visit to the city by Mexican President Felipe Calderon, who will make his third tour this year of the country's most violent city to discuss the government's efforts to tackle organised crime.
Mexico is battling a drug war that has killed some 18,000 people since 2006.
Ciudad Juarez is a major flashpoint in the battle between Mexican drug gangs over trafficking routes to the US. More than 2,600 people were murdered there in drug-related violence last year alone.