As President Carter prepares to announce his plan Monday to save American cities, the administration released a survey yesterday showing a lot of people living in them want to move out.

A Louis Harris survey commissioned by the Department of Housing and Urban Development said that 35 percent of city dwellers said they definitely or probably will move in the next two or three years and that 53 percent of those people plan to live in a suburb or rural area.

"For cities alone, this trend translates into a 10 percent drop" every two years, Harris said. "If that continued another 20 years, then by the end of the century, cities would have fully 50 percent less population than they now have."

Census Bureau officials said they doubt that there will be such a steep rate of decline and added that most cities up to 1 million population are still growing.

However, Harris' attitude survey follows a recent study of major corporations indicating that big business is not willing to make much of a commitment to troubled central cities, and both reports have great implications for Carter's urban plan.

The president's message is expected to stress ways to stop the population outflow from cities and to induce business to remain or move in.

The survey of 352 of the country's largest firms released by Rep. Henry S. Reuss (D-Wis.) last weekend showed many reluctant to locate in central cities because of antipollution rules, high taxes, crime, land prices, and lack of decent schools.

Harris' survey, in which 7,074 adults representing a cross-section of the population were interviewed for one hour, predicted "continued population migration out of the city . . . into towns and rural areas primarily and the suburbs secondarily."

Harris said in a telephone interview that his study indicates cities are becoming the "hub of activity, the social center of the country rather than the residential locus."

A disturbing finding, he said, is that among city dwellers, 47 percent of those under 30 - "the rising middle class with children" - are thinking of moving out. "The key is public schools," he said.

Harris noted that a further loss of middle-income families will mean a continued declining tax base for cities. He said they "can make an excellent case for more money by saying, 'We're being used as centers for medical care, jobs, culture, shopping and recreation, but we're not getting enough money to keep up the support services - street maintenance, lighting, fire, and police - for those activities."

He also said his survey discovered other attitudes that might signal a turnaround in cities' out-migration.

Nationally, of the families who say they want to move, 11 percent say they will move out of suburbia and 9 percent say they will move in, he said. "So suburban growth may have reached its zenith. Small towns and rural areas stand to be the big gainer, but there seems to be a trade-off.

"We asked people to tell whether they wanted a less desirable home closer to their job or a more desirable job an hour away from it," he continued. "By a 46 to 35 percent margin, people picked the more desirable home. But when we asked if they wanted it 1 1/2 hours away from the job, people picked a less desirable home by a 53 to 24 percent margin. So as suburbs get more dense, people may opt for city life over the idyllic but far-off countryside."

The Harris survey found that 55 percent of the public, in and ot of cities, feel that "America would be worse off without cities."

It also found that people gave cities high marks for cultural opportunities, public transportation, movies, restaurants, health facilities, job opportunities, colleges, and shopping.

"But when asked where the best housing is, people selected the suburbs first at 43 percent, the cities second at 22 percent, then towns and rural areas at 18 percent," Harris said.

"On the worst housing the cities finished first handily with 64 percent. Thus, on the surface, the suburbs would appear to have a dominance in the housing area. However, when people were asked which has 'the widest range of housing that you can afford,' the cities emerged in first place, named by 33 percent, with the suburbs second at 27 percent, and towns and rural areas last at 23 percent."

Harris cited three major areas in which cities are "clearly in trouble": they are perceived "as being wracked with crime" (92 percent), as the worst places for raising children (83 percent), and "as centers for racial conflict." In the third category the study did not cite any figures, but it said 76 percent of whites say "they prefer mostly or all-white neighborhoods."

It also found that "city blacks are the most positive about large cities. More than half of city blacks - 53 percent compared to only 35 percent of city whites - list large cities as their top choice" to live.

Harris and Census officials said that despite the anticity attitudes expressed by many who plan to move, no exodus is expected. "You can't overlook inertia," said Census official Richard A. Engels. "Often it's too much of a hassle to find a job and maintain your lifestyle elsewhere."

HUD Secretary Patricia Roberts Harris, who commissioned the $239,000 attitude survey, said it "highlights the interdependence of urban, suburban and rural areas. Many of the people who live in suburban and rural locations make use of nearby cities for economic, social and cultural purposes. Clearly, these cities are essential and far from irrelevant to the lives of those who reside in surrounding areas."