President Carter asked the American people last night to help him build a "new foundation" for the country, recognizing the limits of government activism at home and of U.S. influence abroad.

The president, delivering his second State of the Union message to a joint session of Congress and a national television audience, outlined his goals for the remainder of his term, beginning with measures to restrain inflation and to win approval of a new strategic arms limitation treaty (SALT) with the Soviet Union.

Carter devoted the longest section of his speech to those two topics, calling on Congress to support his "stringent but fair budget," and promising the American people a SALT agreement under which "our deterrent force will remain overwhelming."

He also mentioned briefly other administration priorities, warning Congress that "the American people have waited long enough" for the government to act to hold down rising hospital costs.

But there were no surprises, either in priorities or in the emphasis Carter placed on holding down government spending and on the upcoming Senate debate over a new SALT agreement.

For a speech advertised in advance as an attempt to voice the main themes of the Carter presidency, the 35-minute address contained little rhetorical flourish. The audience in the crowded House chamber interrupted Carter numerous times with polite applause as he flashed his familiar grin through his delivery.

The speech, with its frequently used slogan of "a new foundation," was an attempt by Carter to sum up his achievements and goals, strongly suggesting an era of limitation.

"Our earliest national commitments, modified and resnaped by succeeding generations, have served us well," he said. "But the problems we face today are different in nature from those that confronted earlier generations of Americans. They are more subtle, more complex, more interrelated. At home, few of these problems can be solved by government alone. Abroad, few of them can be solved by the United States alone."

To succeed in fighting inflation, the president said, "We must change our attitudes as well as our policies. We cannot afford to live beyond our means, to create programs we can neither manage nor finance, or to waste our natural resources. And we connot tolerate mismanagement and fraud."

While bowing to earlier social welfare achievements, many of them accomplished by other Democratic presidents, he added: "But it is not enought to have created a lot of government programs. Now we must make the good programs more effective, and improve or weed out those which are wasteful or unnecessary."

On foreign policy, Carter struck much the same theme. Noting changes borught on by the emergence of the Third World, he said, "In such a world, the choice is not which superpower will dominate the world. None can and will. The choice instead is between a world of anarchy and destruction, or a world of cooperation and peace."

White House officials said before the speech that the slogan "a new foundation" was "not an effort at [creating] a catchy phrase." Rather, they said, it reflects Carter's determination "to build new foundations in some of the quicksand we inherited" by seeking sustained but necessarily slower economic growth and by tackling such unglamorous problems as government reorganization and management.

The president clearly placed the anti-inflation campaign at the top of his domestic agenda, beginning with administration efforts to hold the line on the fiscal 1980 budget. That budget was sent to Congress Monday, and has drawn fire from liberals, because of proposed cuts in social welfare programs, and from conservatives, who say Carter is seeking too much spending.

"Business and labor have been increasingly supportive" in the anti-inflation effort, the president said. "It is imperative that we in government do our part. We must stop excessive government growth, and control spending habits."

Voicing the central economic gamble he and his advisers have taken in the budget, he said, "The 1980 budget provides enough spendiing restraint to begin unwinding inflation, but enough support to keep American workers productive and to encourage investment to provide new jobs."

While Carter emphasized the budget, he mentioned only in passing one of its most controversial sections -- the proposed 3 percent increase above the inflation rate in defense spending. He said the United States "must maintain our strategic capability" and asked Congress to support "the strong defense budget I have proposed."

Overall, the president gave scant mention to military and defense matters as he emphasized themes of international cooperation.

Carter made his strongest appeal during the speech on the SALT agreement, signaling the official opening of the administration's campaign to gain Senate approval of the accord once it is signed.

"In this year, 1979," he said, "nothing is more important than that the Congress and the people of the United States resolve to continue with me on that path of nuclear arms control and peace. This is paramount."

Administration officials yesterday refused to speculate on when a signing ceremony, and a summit conference between Carter and Soviet leader Leonid I. Brezhnev, might take place. But a senior White House official noted before the speech that, "The number of issues left is small, and the nature of those issues is not very significant."

"SALT II is not based on sentiment," the president said in making his plea for Senate approval. "It is based on self-interest -- of the United States and the Soviet Union. Both nations share a powerful common interest in reducing the threat of a nuclear war. I will sign no agreement which does not enhance our national security."

Saying that a SALT agreement "will not rely on trust," Carter said, "I will sign no agreement which connot be verified.

"The American muclear deterrent will remain strong after SALT II," he added. "Our deterrent is overwhelming -- and I will sign no agreement unless our deterrent force will remain overwhelming."

The president made only the briefest mention of some countries (notably Iran), that trouble American foreign policy. But a senior White House official said this reflected only the rapidly changing developments in that strife-torn nation.

Reaffirming that "our firm commitment to Israel's survival and security," Carter pledged "to use the full benefical influence of the United States to obtain a peace treaty between Israel and Egypt.

However, White House officials cautioned that the president did not mean to suggest that he is ready to call a second summit conference with Egyptian President Anwar Sadat and Israeli Prime Minister Menachem Begin to break the deadlock that has developed since September's Camp David summit.

Carter also reaffirmed his commitment to human rights.

"The values on which our nation was founded -- individual liberty, selfdetermination, the potential for human fulfillment in freedom -- all of these endure," he said. "We find these democratic principles praised even in books smuggled out of totalitarian nations and on wall posters in lands we thought were closed to our influence."

The president did not describe in detail the legislative proposals he will make to Congress this year. But, mentioning the top administration priorities, Carter:

Promised that "this year we will take our first steps to develop a national health plan." However, White House officials said no decisions have been made on how ambitious a proposal will be developed.

Said enactment of new plans to deregulate elements of the economy -- for example, the surface transportation system -- will help in the anti-inflation fight. "America has the greatest economic system in the world," he said. "Let's reduce government interference and give it a chance to work."

Called for major reorganizations of government programs in education, economic development and natural resources. The president is committed to submitting to Congress, as he did unsuccessfully last year, legislation that would create a department of education. But White House officials said he has not yet decided whether to propose new Cabinet departments to deal with economic development and natural resources.

Asked Congress to approve a new multilateral trade agreement, now in the final stages of negotiations, and legislation establishing new relations with Taiwan following U.S. recognition of the People's Republic of China.

"The new foundation I have discussed tonight," Carter said in returning to his message's slogan, "can help us build a nation and a world where every child is nurtured and can look to the future with hope... I can help us build a nation and a world where all people are free to seek the truth and to add to human understanding, so that all of us may live our lives in peace."