Americans are living longer, and the gap between the life expectancy of whites and blacks is narrowing. But infant death rates -- while at a record low -- are declining more slowly than before, and mortality among black infants remains about twice as high as that for white infants, the government reported yesterday.

"Our nation's 'health grades' are very good indeed," said Health and Human Services Secretary Margaret M. Heckler, as she released her department's annual report card on the nation's health. "And most important of all, further progress on almost every health front is indicated."

Heckler noted that life expectancy at birth reached nearly 75 years in 1983 -- "a record high." But, she added, "More encouraging is the fact that the longstanding disparity between life expectancy for white and black Americans is now narrowing."

The four-year increase in overall life expectancy achieved between 1970 and 1983 was greater than in the preceding two decades. While the increase among whites during this period was 3.5 years, up to 75.2 years, it was greater among blacks, with a rise of 5.5 years to a life expectancy of 69.6 years, the new report said.

Most of the recent life-expectancy gain came among middle-aged and elderly people. The government projects that, on average, Americans who reached age 65 in 1983 could expect to live another 16.8 years, or to nearly age 82. Those who turned 45 that year could expect to live another 33 years, to age 78.

Heckler credited the trend to healthier life styles. This also may have contributed to what she called the "remarkable progress against heart disease and stroke," with heart-disease mortality down 25 percent since 1970 and stroke deaths down almost 50 percent.

Health experts say they believe that the incidence of such deaths has declined, at least in part because of wider use of drugs to control high blood pressure, improved diet, increased exercise, less smoking and generally better preventive and therapeutic health care.

"There are, of course, lags and aberrations. We certainly cannot rest on our laurels," Heckler said in the introduction to the report, "Health, United States, 1984." In her news conference yesterday, she acknowledged two particular concerns: slowing progress in the fight against infant mortality and increased lung cancer among women smokers.

Heckler said the national infant mortality rate "continues to show improvement," falling to 10.9 deaths per thousand live births in 1983. Provisional data for 1984 shows a "further decrease," she said, to 10.6, about a 3 percent decrease.

Experts from the National Center for Health Statistics, which prepared the report, said that although often there is a fluctuation from year to year, the 1983 and 1984 numbers represent "the first time that we saw two slow declines in a row." They said that at least seven states were having particular problems.

Heckler said yesterday that the HHS would do more to prevent infant mortality, including measures ranging from spending available funds to sending Public Health Service "Infant Mortality Review Teams" to states that ask for help.

She said she would seek a new public information campaign to help inform women of the health consequences of smoking during pregnancy. Smoking can increase the chances of delivering a low-birthweight baby who is more prone to early death, suffering complications during pregnancy and delivering prematurely. Yet, noted Heckler, 44 percent of married women with less than a high school education smoked during pregnancy in 1980, as did 28 percent of high school graduates and 16 percent of those who had completed some college.

Heckler contended that the country will succeed in meeting the U.S. surgeon general's 1990 goal of reducing infant mortality in the first year of life to 9 deaths per thousand live births. But she acknowledged that it would be "more difficult to achieve" the goal of 12 deaths per thousand births among minority infants. In 1982, the most recent year for which data is available, black infant mortality was 19.6 deaths per thousand births.

Congressional critics and groups such as the Children's Defense Fund question whether the United States will meet the 1990 goals. They have criticized the Reagan administration's budget cuts and say that more should be spent to care for pregnant women and their newborn children.

Heckler also noted that "lung cancer is rapidly approaching breast cancer as the leading cause of cancer deaths among American women. In fact, among those aged 55 to 74, lung-cancer mortality has already overtaken the death rate for breast cancer." About 30 percent of adult women smoke.

Other findings of the 188-page report include:

* Life expectancy. In addition to a narrowing in the racial gap, the life-expectancy differences between the sexes is narrowing. Nonetheless, in 1983, female life expectancy at birth -- 78.3 years -- exceeded that for males by 7.3 years.

* Infant mortality. Despite a nearly 50 percent decline since the mid-1960's, the U.S. infant mortality rate still falls behind most industrialized countries. There is wide variation among states, ranging in 1983 from 9 in Vermont to 12.5 in West Virginia per thousand live births among whites. Among black infant births, it swings from 16.4 (Massachusetts) to 25.9 (Illinois) in the 26 states with black populations of 150,000 or more.

The District has a higher black infant-mortality rate -- 26.3 -- than any state, as well as a higher white infant mortality rate of 13.7 (this may be unreliable because of the small number of white births). Despite this, Heckler said yesterday that recent improvements -- a 35 percent reduction over three years -- showed "dramatic progress."

* Motor vehicle accident death rates. Among males between age 15 and 24, the overall rate for whites -- 67.6 per 100,000 in 1981 -- was about twice as high as the rate for blacks -- 30.8. The rates were highest among white males in three states, Wyoming, Nevada and New Mexico; and highest among black males in Mississippi and South Carolina.