Myrlie Evers, wife of slain civil rights leader Medgar Evers, asked a University of Utah audience to continue the work of Martin Luther King Jr. every day, not just one or two weeks a year.

"We cannot be a great democracy as long as even one small segment of our population is not allowed to be free," said Evers, whose husband was shot in the back 25 years ago outside his Mississippi home.Evers, speaking during Martin Luther King Day activities at the university Friday, asked the audience to remember King as a leader "who challenged us individually and as a group . . . to look into our own hearts and see if there was any trace of racism there."

She also said she was concerned that the gains of the civil rights movement and the concerns for equal justice that arose during the 1960s have lapsed.

"There are so many today who say we have arrived, we are here, but what about those invisible barriers," she said. Evers said there remained unequal salaries for minorities, and President Reagan's administration has worked to do away with affirmative action.

"Reagan has all but encouraged that we eliminate affirmative action," she said. "It sends a message to state and local governments that things need not change and that things may slip back to the way they once were."

Evers said she was concerned that racial injustices of 1960s have become a "fire smoldering in grief which cooled down only to perhaps burst into flame again."

Medgar Evers was a civil rights leader in Mississippi who laid the ground for King's civil rights campaign. He was field secretary for the National Association for the Advancement of Colored People until he was shot in the back on June 12, 1963, at his home in Mississippi.

Evers quoted her husband as once saying, "I will give my life and I will give it gladly so that my wife and children . . . and others can have the life they deserve."

She also said she was disturbed about such movies as "Mississippi Burning," which she called "a very powerful movie in its fiction - and I stress its fiction.

"As I watched the burnings and as I watched the beatings, I said `yes, that is true,' and I also remembered people of other colors helping us," she said, adding that she finds fault because it makes heroes out of two FBI agents.

"At that time the FBI . . . was not there to protect us," she said. "They watched and they aided the other side."