LA UNIÓN, Mexico — Gunmen believed to be linked to drug traffickers shot a pregnant American consulate worker and her husband to death in the violence-racked border town of Ciudad Juárez over the weekend, leaving their baby wailing in the back seat of their car, the authorities said Sunday. The gunmen also killed the husband of another consular employee and wounded his two young children.

The shootings took place minutes apart and appeared to be the first deadly attacks on American officials and their families by Mexico’s powerful drug organizations, provoking an angry reaction from the White House. They came during a particularly bloody weekend when nearly 50 people were killed nationwide in drug-gang violence, including attacks in Acapulco as American college students began arriving for spring break.

The killings followed threats against American diplomats along the Mexican border and complaints from consulate workers that drug-related violence was growing untenable, American officials said. Even before the shootings, the State Department had quietly made the decision to allow consulate workers to evacuate their families across the border to the United States.

In Washington, President Obama denounced the “brutal murders” and vowed to “work tirelessly” with Mexican law enforcement officials to prosecute the killers. Secretary of State Hillary Rodham Clinton said the killings underscored the need to work with the Mexican government “to cripple the influence of trafficking organizations at work in Mexico.”