Editor's note: The following story contains language some readers may consider offensive. Read the lawsuit filed in court on Tuesday here.

Jackson, Mississippi (CNN) -- The family of an African-American man who was killed when he was beaten and run over with a truck has filed a wrongful death lawsuit against a group of teens alleged to have been present at the time of the attack.

The lawsuit -- filed Tuesday in a Mississippi district court -- alleges that seven white teenagers "set out on a mission" to find and harass African-Americans.

The lawsuit, filed by the victim's sister, mother and two brothers, seeks a jury trial and damages. It names not only the two teens facing criminal charges in the incident but others who, the suit alleges, acted as lookouts and prevented Anderson from escaping.

The death of James Craig Anderson, 48, occurred early June 26 in Jackson, Mississippi -- allegedly at the hands of white teens who, after a night of partying and drinking, decided to "go fuck with some niggers," police said, quoting one of the suspects in the case.

"James Anderson lost his life for no other reason than the color of his skin," said Morris Dees, chief trial counsel for the Montgomery, Alabama-based Southern Poverty Law Center, in a statement. The law center filed the suit on Anderson's family's behalf along with Mississippi attorney Winston J. Thompson III. "Those responsible must be held accountable for their callous and deadly actions. We are filing this lawsuit today to ensure his family gets a measure of justice."

Anderson's death drew national attention after CNN first reported it and aired exclusive surveillance video of the killing in a Jackson suburb. Hinds County, Mississippi, District Attorney Robert Shuler Smith, who is prosecuting the case, has called it "vicious" and a "premeditated hate crime."

U.S. Department of Justice investigators are now in Jackson, investigating the death as a possible federal hate crime and assisting local prosecutors.

The killing has also prompted several large marches and prayer vigils in Jackson, a city of about 537,000 people. Thompson said there has been an "outpouring of support" for the Anderson family from the area.

"This isn't just something that happens in Mississippi," Dees told reporters Tuesday at a news conference announcing the filing of the suit. "This is something that's happening all across the nation. We feel like this case is particularly egregious."

Deryl Dedmon Jr., 19, of Brandon, Mississippi, is facing capital murder charges in Anderson's death and is eligible for the death penalty. A second teen, John Aaron Rice, 18, was initially charged with murder, but a judge reduced the charges to simple assault because Rice was not believed to be driving the vehicle used to kill Anderson.

However, Hinds County prosecutors said they plan to seek indictments against both Dedmon and Rice for murder and a hate crime, and also will seek indictments against other teens who were at the scene. Neither teen has issued a plea.

A pretrial hearing for Dedmon was postponed Tuesday afternoon, based on a defense request. No reason was given. The hearing was rescheduled for September 26.

The five other teens who took part in the incident that evening, according to the suit, are: Sarah Graves, of Crystal Springs; Shelbie Richards, of Pearl; and William Kirk Montgomery, John Blaylock and Dylan Butler, all of Brandon. None of the five has been arrested or charged, and it was unclear Tuesday whether they had retained attorneys.

Anderson's family did not attend Tuesday's news conference. Thompson told reporters they were "still grieving" but awaiting the results of the criminal investigation.

Anderson, a line worker at a Nissan plant, sang in his church choir, Thompson told reporters. He leaves behind his partner of 17 years.

"He was just a pillar of the community," Thompson said. "He paid his taxes on time, he went to work, came home -- he was just an average, ordinary citizen, good guy, wonderful gardener."

"Anyone who knew James could see that he was a caring man with a beautiful smile," said Barbara Anderson Young, Anderson's sister, in a statement. "He was such a compassionate person. We must take an honest look at the racial climate that motivated some young people to hurt such a wonderful person."

Attorneys for Dedmon and Rice have not responded to requests for comment from CNN. During a bond hearing, Dedmon's attorney told the court he saw nothing to back up the "racial allegations."

But "Dedmon murdered this man because he was black," Smith said. "The evidence will show that."

A civil trial can proceed at the same time as a criminal case, but often the civil case is delayed pending the resolution of a criminal trial. While a criminal case is pending, a defendant in a civil case may need to invoke the Fifth Amendment.

Thompson said Tuesday the civil case will be pursued in conjunction with the criminal case. If attorneys for Dedmon and Rice file a motion to stay the suit pending the outcome of a criminal trial, "then we'll take that up with the judge."

The suit alleges all seven of the teens "took part in what we call a joint venture, to seek out and do harm to a person of color," Thompson said.

He said after the news conference that filing the suit will allow attorneys to conduct discovery, take some depositions and hopefully find out from all seven teens what took place the night Anderson died. Anderson's family is hopeful, at the conclusion of local and federal investigations, that all those culpable in his death will be charged, he said.

Dees told reporters Tuesday that even if the teens did not participate in Anderson's beating or in striking him with the vehicle, they can still be liable under the law for failing to stop the beating or assist Anderson.

Authorities believe Dedmon led and instigated the attack, which took place after a night of drinking in largely white Rankin County outside Jackson. Dedmon told friends they should leave, saying, "Let's go fuck with some niggers," officials said.

The gang of teens climbed into Dedmon's green truck and a white SUV and drove 16 miles to the western edge of Jackson. They would have seen Anderson immediately as they exited the highway, officials said. He was standing in a hotel parking lot just beyond the exit ramp.

On the videotape obtained by CNN, the group of teens is seen pulling into the parking lot and stopping where Anderson is standing, although he is just off camera and not visible.

The teens can then be seen going back and forth between their cars and Anderson. Witnesses told authorities this is when Anderson's beating took place, as the teens yelled racial epithets including "white power."

Authorities allege Dedmon pummeled Anderson repeatedly as he crumpled to the ground, although this is not visible on the tape. After the beating, some of the teens left and others got into the green truck.

At this moment, Anderson becomes visible on the tape as he staggers into view and walked toward the truck.

"Defendant Dedmon drove the F-250 out of the parking lot and turned right onto Ellis Avenue," the lawsuit says. "Just as Dedmon turned right, his headlights shone directly on Anderson, who, having been severely beaten, was stumbling in a grassy are near the motel's entrance. Dedmon accelerated, drove onto and over the street curb, and struck Anderson with the front of the F-250."

Shortly afterward, Dedmon allegedly boasted and laughed about the killing, according to statements some of the teens made to detectives. "I ran that nigger over," he allegedly said in a phone conversation to the teens in the other car.

"He was not remorseful," Smith said. "He was laughing, laughing about the killing."

Thompson said Tuesday it was unclear why Anderson was at the hotel, but he was believed to be heading toward his truck when the incident took place.

At Dedmon's home last month, a girl who answered the door told CNN she did not know him, although a truck like the one allegedly used to strike Anderson was sticking out of the garage.

Dees noted the attorneys spoke to reporters in front of the Hinds County courthouse, where in 1994 Byron de la Beckwith was convicted of killing civil rights leader Medgar Evers in 1963, and talking about a similarly "horrendous" crime.

"Because it's coming out of Mississippi, and out of Hinds County, I think it will resonate around the country," he said.

CNN's Ashley Hayes contributed to this report.