The nation's colleges and high schools lack a sufficient number of qualified athletic trainers who could aid in preventing and treating an estimated 1 million sports-related injuries annually, according to a government report released yesterday.

An estimated 111,000 of those injuries were deemed serious -- forcing a student to miss at least three weeks of practice or classes -- and varsity football accounted for 325,000 of the total number of injuries.

Additionally, the overall football injury rate for high school and college athletes was 280 per 1,000 players. But at four-year colleges, the report said, that injury rate was 929 per 1,000 participants. Those injuries ran the gamut from minor bumps and bruises to major medical problems.

These were some of the key findings in a $40,000 survey on athletic injuries made during the 1975-76 school year for the Department of Health, Education and Welfare.

"Many of the injuries the report documents might have been prevented if schools used safer equipment, if coaches and trainers were better trained in preventing as well as promptly treating injuries, and if participants had been taught safety rules as well as the rules of the game," HEW Secretary Joseph A. Califano Jr. said in a statement released with the report.

Congress ordered the survey in response to a bill sponsored by Rep. Ronald Dellums (D-Calif.) that would have required trainers to be present at all high school and college games.

There are no startingly new conclusions in the report. Researchers found, for example, that football is the most dangerous sport and that contact sports are more perilous than noncontact sports.

While the report contains no specific recommendations, Califano said he would ask the nation's school officers to review their athletic programs to explore ways to make them safer. Casualties, he said, may be at "unacceptably high levels."

The report notes that logistical problems -- every state was surveyed -- and financial restraints -- only $75,000 of the cost went to the project, the rest to salaries -- precluded a fully comprehensive survey. But, the report continues, the figures developed provide a substantial base for projections and further study.

The survey was based on reports from 1,298 colleges and 2,554 high schools in the 1976 academic year when participation by female athletes was just beginning to increase rapidly because of a federal anti-bias law.

While there is an overlapping number of participants, the report said 4.1 million men and 1.6 million women played varsity sports at both the collegiate and secondary levels. Corresponding figures were 3.3 million men and 1.8 million women participating in intramurals and 6 million men and 5.7 million women in physical education classes.

There were an estimated 1 million injuries, classified as major (out 20 or more days, 111,098) and minor (out fewer than 20 days, 704,307).

There were also 14 sports-related deaths in the study year: four from tackle football, four from other contact sports, three from noncontact sports and three from physical education programs, including the lone female death.

Varsity football, played by 1.1 million males, accounted for 325,000 of the total injuries; the rate of football injuries was 280 per 1,000 participants, four times higher than in noncontact sports.

Injury rates in other contact sports were 74 per 1,000 for men and 54 per 1,000 for women. In noncontact sports, the rates were 38 per 1,000for men and 32 per for 1,000 for women. Women represented 28.7 percent of the varsity participants and 15.9 percent of injuries.

The overwhelming number of injuries occurred when a "health care person" was "available." Here, the report found there were differing interpretations of those words.

The report found that 96 percent of the colleges and high schools have someone responsible for the immediate care of injuries. However, that person usually is a coach (70.3 percent of the schools), or school nurse (5.2 percent), instead of an accredited trainer (13.9 percent).

A sample of 456 coaches listed as the prime source of health care showed that 47 percent had not taken the required advanced first aid or other work to qualify for their duties, the report states.

The report defines certification by or membership in the National Athletic Trainers Association as an "index of competence." Only 5 percent of the high school, 7 percent of the two-year colleges and 28 percent of the four-year colleges had NATA-accredited trainers.

When non-NATA trainers are included, the percentage of schools with trainers is: public highs, 10.9 private highs, 15.4; two-year colleges, 16.1, and four-year colleges, 40.2. Two-thirds of all four-year colleges that offer football, however, have trainers.

Mandated by Congress in 1974, the survey was conducted by the National Center for Education Statistics in conjunction with the National Athletic Injury/Illness Reporting System at Pennsylvania State University.