Attorney General William French Smith yesterday called family violence in America a "serious and complex crime problem" and named a federal task force to study how the federal and state governments can deal with it.

"The incalculable costs of these crimes in physical and emotional suffering, ruined lives and future crimes are intolerable in our civilized society," Smith said, noting that domestic violence has been seen as a "private matter" best handled outside the legal system.

"Because of the complexities of family violence and the significant ways in which its causes and its solutions seem to differ from other criminal behavior, the federal government must take a leading role in this area," Smith said.

Assistant Attorney General Lois Herrington, who will oversee the task force's work, described family violence as a "time bomb . . . . Children raised in violent homes become abusers and violent criminals in the next generation."

There is little federal jurisdiction over family violence, but Smith said the task force will "finally place the problem of family violence in its proper perspective in the criminal justice system."

He said the task force, which will meet and hold hearings over a six-month period, will concentrate on physical and sexual child abuse, spouse abuse and mistreatment of the elderly.

Smith's action is expected to anger conservative groups that oppose further government intervention in family affairs as an infringement of parental rights.

Connie Marshner, chairman of the National Pro-Family Coalition, said the new task force "seems to be window dressing to placate the gender gap."

But Herrington, head of the department's Office of Justice Assistance, Research and Statistics, said that the task force was not created to improve the administration's image among female voters. "It is not a political issue," she said.

Although there are few statistics on family violence and many cases are believed to be unreported, Herrington said reported cases of child victimization doubled to 850,000 between 1976 and 1981, while a federal study showed that arrests in family-related offenses declined by 24 percent between 1973 and 1982.

Herrington said the task force was prompted by a special task force on victims of crime, which earlier this year recommended creating a panel to review violence in American families.

"This problem was so big, and the magnitude so enormous, that we were stunned," she said.

Detroit Police Chief William Hart, who previously served on Smith's Task Force on Violent Crime, was named to head the task force.

Members of the task force include Missouri Attorney General John Ashcroft; Ursula Meese, wife of presidential counselor Edwin Meese III; Ann Burgess, associate director of nursing research at Boston City Hospital; Frances Seward, safety director of the Jamaica Services Program for Older Adults in New York, and Catherine Milton, a researcher and author on law enforcement and victims issues and assistant to the president of Stanford University.

Other members include Clyde Narramore, a Christian psychologist and a family and marriage counselor, Phoenix Police Chief Reuben Ortega and Newman Flanagan, district attorney of Suffolk County, Mass.

Smith said the task force will have a $500,000 budget.