The former president has said through representatives in La Paz that he does not intend to return to Bolivia until the country's justice system can guarantee him a fair trial.
Another lawsuit with the same charges was filed against Carlos Sanchez Berzain, a former interior and defence minister.
Sonia Espejos, the widow of a man killed during the protests, said: "They are the only ones responsible for what we are suffering here in Bolivia. We are not going to allow Gonzalo Sanchez de Lozada to tour the United States.
The US-based Centre for Constitutional Rights (CCR), which is representing the plaintiffs, said in a statement: "The suits ... charge Sanchez de Lozada and Sanchez Berzain with extra-judicial killings and crimes against humanity for their role in the massacre of unarmed civilians, including children."
In a recent interview with local radio station Fides, Sanchez Berzain said he was the victim of political persecution.
Among the plaintiffs in the case are Eloy Rojas and Etelvina Ramos, whose eight-year-old daughter was killed when a single shot was fired through their window, and Teofilo Baltazar, whose pregnant wife was killed after a bullet tore through the wall of a house, the CCR said.
Earlier this month, Bolivia's highest court asked the government to start extradition proceedings against Sanchez de Lozada, but representatives of the victims say they do not have faith in the country's justice system.
Rogelio Maita, a lawyer working for the October 2003 Victims Association, said the lawsuits were "the best alternative that we have for justice to be carried out".