An election-minded White House yesterday moved to neutralize yet another domestic issue on which President Reagan has been under attack--hunger in America--by announcing creation of a task force to study the problem and promising the distribution of more free food to the poor.

In a flurry of related activity, the House overwhelmingly approved a non-binding resolution, sponsored by more than 200 House members and a majority of the Senate, opposing any further budget cuts in federal nutrition programs this year or next.

The U.S. Conference of Mayors, chiding Reagan for previous budget cuts in food programs, said it has drafted a seven-point program to ease the hunger of an estimated 40 million Americans. And three Senate Republicans introduced legislation to further tighten food stamp requirements.

The White House, anticipating that Democrats might seize the hunger issue in next year's presidential campaign, appeared to be launching a pre-emptive strike yesterday as part of a larger administration effort to blunt the perception that Reagan's programs have been unfair to the poor and disadvantaged.

In a memorandum to White House counselor Edwin Meese III, Reagan said he was "deeply concerned" about the hunger problem and asked for a 90-day study to determine why people are hungry and what the federal government can do about it.

Reagan, who in the last 2 1/2 years asked Congress to tighten the eligibility for food stamps and to slow the growth in other federal nutrition programs, said he has been "perplexed" by news accounts about hunger because he thought the government was taking care of those in need. Reagan declared that "I intend to find out" why federal programs are not reaching hungry people.

At the same time, Agriculture Secretary John R. Block said the administration will increase the distribution of surplus cheese and also give away free butter, dry milk, cornmeal and honey to poor people.

A department spokesman said details of the food giveaway were still being worked out last night. Block said in Nashville on Monday that bulk surplus food would be given to the states and they would have it processed before distribution to the poor.

That announcement ended a short sit-in by protestors at the Agriculture Department who were seeking increased government food distribution. The protest was organized by the same group that has refused to eat since July 4 in Kansas City in a demand for more government food distribution.

The White House offensive on the hunger issue comes on the heels of similar efforts to demonstrate Reagan's concern for education, civil rights and the problems of women and minorities. But some White House officials had earlier expressed private doubts about the hunger effort because it would appear to run contradictory to Reagan's repeated efforts to restrain the cost of federal food and nutrition programs.

At the outset of his term, Reagan proposed tightening the eligibility of food stamps, and Congress agreed to limit the benefits to persons who have incomes of no more than 130 percent of the poverty level. For 1983-84, the poverty level is $9,862 for a family of four.

But largely because of the recession, the number of Americans relying on the food stamp program has expanded. An estimated 22 million people receive food stamp benefits. Thus, while more people are receiving food stamps than before, the requirements for eligibility are stricter than when the Reagan program began.

Reagan has proposed further restrictions on the food stamp program for next fiscal year, but Congress is not expected to approve them. The president made no mention of his past or pending budget reductions in the letter yesterday. He declared it would be a "national tragedy" if "even one American child is forced to go to bed hungry at night, or if one senior citizen is denied the dignity of proper nutrition."

The announcement of the task force--to include between nine and 12 members, all outside the administration--was greeted skeptically by some critics of administration food and nutrition policy.

"I think it's very belated," said Carolyn Brickey, a lawyer Food Reaseach Action Council lobbyist. "Hunger is something they should have been researching a long time ago when they were proposing those very Draconian budget cuts."

Robert B. Carleson, a special assistant to the president, said Reagan may consider spending more money on the hunger problem if the task force finds it is warranted. The task force is also supposed to determine if food programs have been mismanaged.