President Reagan and House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) took their weekly boxing match onto national radio yesterday, with Reagan saying "things are looking up" now that the economy is recovering and O'Neill countering that 15 percent of the population now lives in poverty.

O'Neill, referrring to Reagan's announcement last week of a commission on hunger and plans to increase the amount of free food distributed by the government, said that if Reagan truly cares for the poor he should rescind some budget cuts that have eliminated aid to the poor.

"The president has declared a new sensitivity to the problems of hunger in America," said O'Neill, after telling listeners of visiting his district in Boston and seeing acquaintances lining up to receive free food.

"There is one specific step he can take to convert this sensitivity into action. He should withdraw his proposed cuts in the nutrition program for women, infants and children . . . . Under his pending request, some 600,000 low-income expectant mothers, infants and children would have to be terminated from this vital program next year. Is that fair? . . . The truth is that our economy does not become richer because we cut programs that help the neediest."

It was one of the few times the Democrats have used the speaker, the titular head of the party, to respond to Reagan's weekly radio address, and O'Neill attacked rather than responded. His speech was prepared and released a day in advance. Meanwhile, Reagan, in a live radio address from Camp David, Md., said his economic policies have prompted a domestic recovery. He said that recovery has eliminated the need for new tariffs and quotas and "dead-end protectionism." He cited a controversial textile agreement signed with China last week that failed to meet requests by U.S. textile manufacturers for further restrictions on textile imports.

"Things are looking up for America," Reagan said. "Inflation has been knocked down to 2.6 percent. Economic growth in the second quarter reached 8.7 percent and 1.7 million Americans have been hired since last December. Yesterday we learned that total unemployment has dropped to 9.3 percent . . . . More Americans are working than any time in this nation's history. This good news restores confidence in our economy and our currency."

Reagan then responded to recent criticism from European leaders that high U.S. interest rates are bolstering the dollar at the expense of their economies. The president said the dollar is strong not because of high interest rates but because of U.S. success in combating inflation.

"Some people dislike our strong dollar and blame it on our interest rates," he said. "We do not want disorderly currency markets and we've intervened to bring back order to otherwise disorderly markets . . . . Other countries have higher interest rates than we do, yet their currencies have fallen in relation to ours. One good reason is inflation.

"It's not the interest you earn from holding a currency that matters most," he added. "It's the confidence you have that the value of your money won't depreciate from higher inflation. America's inflation rate has declined dramatically."

Reagan also noted that the strength of the dollar has hurt U.S. exports. But he said U.S. businesses can still be "tough competitors."

"So," the president asked, "do we go back to the dead-end protectionism and to sabotaging the value of our currency, or do we go forward?"

Last week Reagan named a Commission on Industrial Competitiveness to counter the push by American business for added protectionist measures by helping domestic industries become more competitive through better use of technology.