In his fifth State of the Union message, President Reagan called last night for an "agenda for the future" that includes many of his past proposals plus new federal studies on the problems of poverty, catastrophic illness and currency instability.

In a nationally televised speech that celebrated American accomplishments and purposefully avoided painful budgetary details, the president urged Congress to cut the domestic budget and continue to increase military spending. He also appealed for passage of "an historic tax reform providing new opportunity for all" and repeated his opposition to tax increases, even though earlier in the day he had opened the door to a possible imposition of an oil import fee.

Reagan told a joint session of Congress that the Gramm-Rudman-Hollings balanced-budget law "gives us an historic opportunity to achieve what has eluded our national leadership for decades -- forcing the federal government to live within its means."

The president pledged his support for arms control and said that "if the Soviet government wants an agreement that truly reduces nuclear arms, there will be an agreement."

Reagan made no mention of the Jan. 15 proposal by Soviet leader Mikhail Gorbachev calling for staged reductions of U.S. and Soviet nuclear arsenals leading to the total elimination of them by the end of the century. The president said at the time he was "grateful" for the proposal, but a senior administration official who briefed reporters on the speech yesterday said that the Soviet proposal was not an "appropriate response" to a U.S. plan for reducing nuclear arsenals.

Reagan's speech was postponed a week because of the explosion of the space shuttle Challenger. Opening his address, Reagan said Americans "mourn and honor the valor of our seven Challenger heroes. And I hope we are now ready to do what they would want us to do -- go forward America, reach for the stars." Later in the speech, Reagan promised: "We are going forward with our shuttle flights; we are going forward to build our space station."

The president then turned to House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.), presiding over his 10th and last State of the Union message because he is retiring at the end of the year. Reagan saluted O'Neill for his service and later appealed to him for support.

"Now, Mr. Speaker, you know, I know, and the American people know -- the federal budget system is broken . . . , " Reagan said. "Before we leave this city, let's you and I work together to fix it so that we can finally give the American people a balanced budget."

"I'm for that, Mr. President," said O'Neill softly from behind the president. O'Neill has been a persistent critic of many of the administration's proposed budget cuts.

Reagan said that the budget he will submit to Congress today "will meet the Gramm-Rudman-Hollings target for deficit reductions; meet our commitment to ensure a strong national defense; meet our commitment to protect Social Security and the less fortunate; and, yes, meet our commitment not to raise taxes."

The president's preference for reductions in domestic rather than military spending was strongly emphasized in a passage in which he spoke of the "Soviet drive for domination" and said, "The Soviets must know that if America reduces her defenses, it will be because of a reduced threat, not a reduced resolve."

Reagan repeated his appeal for a missile defense plan, which he referred to as "a security shield [that] can one day render nuclear weapons obsolete and free mankind from the prison of nuclear terror." The Soviets have insisted that the proposal, the Strategic Defense Initiative, is a barrier to an agreement limiting offensive nuclear weapons, and domestic critics of the plan have questioned its feasibility.

The president also repeated his support for insurgents -- all of whom the administation is aiding financially -- opposing communist or leftist regimes in Afghanistan, Angola, Cambodia and Nicaragua. "We say to you tonight -- you are not alone freedom fighters," Reagan said.

Reagan, a longtime opponent of protectionist measures, once more declared his preference for "freer and fairer trade." But he acknowledged problems arising from the strong U.S. dollar but did not directly say it is overvalued. Calling for "a sound and stable dollar at home and reliable exchange rates around the world," Reagan said he is directing Treasury Secretary James A. Baker III to determine whether there should be an international monetary conference.

Of the new proposals made by Reagan last night, the potentially most far-reaching is a year-long study he ordered undertaken by the White House Domestic Council headed by Attorney General Edwin Meese III. The president said this study will evaluate programs and develop "a strategy for immediate action to meet the financial, educational, social and safety concerns of poor people."

Reagan was strongly applauded when he concluded this passage by saying "the success of welfare should be judged by how many of its recipients become independent of welfare."

The president said that "in the welfare culture" the breakdown of the family has "reached crisis proportions in female and child poverty, child abandonment, horrible crimes and deteriorating schools."

Reagan repeated his opposition to abortion, saying that "America will never be whole as long as the right to life granted by our Creator is denied to the unborn." Antiabortion groups had urged the president to include this message in his speech, and White House sources said Reagan had decided in their favor after a disagreement among his aides on this issue.

Officials who briefed reporters on the speech denied that the study directed by Meese will be used as a device to reduce services for the poor. But they disagreed on how much these services cost.

The president's other new proposal, one he has favored since he was governor of California, is a study that will be directed by Health and Human Services Secretary Otis R. Bowen on ways to provide affordable health insurance for Americans "whose life savings would otherwise be threatened when catastrophic illness strikes." The administration is expected to ask Congress soon to expand Medicare to cover catastrophic illness costs for the elderly.

Reagan was warmly applauded when he entered and left the House chamber, and his speech was interrupted by applause 28 times.

He ended his message by lauding the accomplishments of four young Americans who were seated with First Lady Nancy Reagan in the House gallery -- science student Richard Cavoli, music prodigy Tyrone Ford, safety patrol member Shelby Butler, who saved another girl in a school bus accident, and Trevor Ferrell, who aided the homeless in suburban Philadelphia. All are 13 years old except Ford, who is 12.

Asking the four to stand, Reagan said, "You are heroes of our hearts. We look at you and know it is true -- in this land of dreams fulfilled where greater dreams may be imagined, nothing is impossible, no victory is beyond our reach, no glory will ever be too great."