The White House, led by President Reagan, is mounting a concerted counteroffensive to dispel a growing impression that administration policies are unfair to poor and needy Americans.

"It's an issue we're sensitive about politically," White House deputy chief of staff Michael K. Deaver said yesterday. "It shows up in the polls and it hurts the president personally because he's a very fair man."

Reagan is now responding to the "fairness" issue in every speech. His staff is actively seeking what an aide calls "people events" like the president's appearance in flood-damaged Fort Wayne, Ind., last week. Cabinet members have been instructed to depict administration economic programs as ultimately helpful to poor people.

"There is growth in programs that help people," said Craig L. Fuller, the White House director of Cabinet administration. "We're trying to get that message out to people who are speaking constantly."

The material given to Cabinet secretaries and other administration spokesmen emphasizes that purchasing power for working people has increased because of a reduction in the rate of inflation.

While there is a frankly political thrust to the administration effort to dispel the belief that Reagan programs are unfair to lower-income Americans, White House officials said the new "fairness" theme basically reflects the president's sensitivity at being depicted as uncaring.

In a speech Tuesday night in New York before the National Conference of Christians and Jews, Reagan freely acknowledged that these criticisms concerned him. "Today I'm accused by some of trying to destroy government's commitment to compassion and to the needy," Reagan said. "Does that bother me? Yes."

The president went on to compare himself to Franklin D. Roosevelt and to say that his policies, like Roosevelt's, are designed to save the free enterprise system and help poor people.

Both in private and public Reagan defends his economic program as offering long-term help to working people and a way out of the recession he blames on his predecessors.

During his recent trip to Alabama, Tennessee and Oklahoma, Reagan described his tax reduction program as "the best darn thing that's been done for working and middle-income people in nearly 20 years" and stressed his "real compassion" for people who cannot help themselves. The tax cut, he said repeatedly, will create jobs and "most of the benefits will go to average citizens in your hometowns."

Reagan's aides recognize that the president's contention that his program will help "average citizens" is being greeted with steadily growing skepticism. Without disclosing the figures, aides said this skepticism has been reflected for several months in polls taken for the Republican National Committee by Richard B. Wirthlin, Reagan's campaign pollster and strategist.

With this in mind, Reagan advisers have stressed proposals, such as the minimum tax for corporations advocated by the president, which they hope will help counteract the idea that administration policies favor the rich.

Reagan in nearly every speech stresses the importance of volunteerism and private charity as a means of filling the gap left by reduction of government programs. His political advisers are looking for events that will show Reagan mingling with ordinary people.

On the president's recent southern swing, aides first considered an event with school children in Alabama and another in an Oklahoma oil field. They settled for Reagan's quick trip to Fort Wayne, where he briefly assisted volunteers stacking sandbags to hold back flood waters.

For security reasons, it is considered unlikely that Reagan will address any crowds of protesting demonstrators, as he used to do when governor of California. The "people events" are likely to be limited to such as Fort Wayne, where there is no prior announcement of the president's plans.