President Carter yesterday signed the historic treaties that would transfer control of the Panama Canal - long a symbol of U.S. power and technological prowess - to Panama by the end of the century.

Carter and Gen. Omar Torrijos, military ruler of Panama, put their signatures on the two, blue-bound treaties in the presence of the assembled presidents, prime ministers and other high officials from 23 other hemispheric nations gathered at the headquarters of the Organization of American States.

The treaties, Carter said, "mark the commitment of the United States to the belief that fairness, no force should lie at the heart of our dealings with the nations of the world."

With these words, the President underscored anew his administration's determination to deal with even the tiniest countries on the basis of "mutual respect and cooperation."

His remarks were also intended to signal to the visiting leaders of Latin America - a region where U.S. control over the canal has been regarded as an archaic vestige of "Yankee imperialism" - that Washington places particular stress on applying this formula to its hemispheric neighbors.

However, the glittering occasion of the signing ceremony and a gala dinner afterwards were not without clearly discernible notes of underlying tension.

The treaties, which must be approved by the Senate before they can be put into effect, face bitter opposition from critics in this country who charge that continued U.S. control is vital to its prestige and military defense.

With an eye toward what is expected to be a prolonged and emotional fight in the Senate, the administration pointedly invited the 100 senators to last night's ceremony in order to spotlight the support that the treaties have from other hemispheric leaders.

Another sign of the continuing discord provoked by the canal issue was the outbreak of bombing incidents, bomb threats, protest marches and other demonstrations that spread like brush fires throughout Washington yesterday.

Some of the protests were directly related to the canal treaties and conducted by Americans who denounced the agreements as a "giveaway" and by Latins who consider the drawn-out timetable for the transfer of control as too minor and meaningless a gesture by the United States.

But most of the demonstrations were staged by Washington's large colony of exiles from Latin America's turbulent politics and were aimed not at the agreement but at the alleged repressive policies of many of the Latin leaders in attendance here.

Last night's ceremony was the centerpiece of Carter's decision to use the canal treaties as an excuse for a summit meeting of hemispheric leaders - one that administration sources say is intended to serve a double-edged purpose.

Most immediately, the gathering of governmental chiefs was calculated to impress on the U.S. public - and its representatives in the Senate - that the canal is the most sensitive issue in U.S.-Latin American relations and that the treaties are backed by a solid front of support among this country's southern neighbors.

That will be the administration's principal arguing point in the impending battle to win Senate approval of the treaties. By surrounding Carter and Torrijos with an approving phalanx of their fellow hemispheric leaders, the signing ceremony was designed to remind wavering senators that rejection of the treaties could send shock waves of disillusionment coursing through Latin America and touch off reactions inimical to U.S. diplomatic, economic and strategic interests in the area.

But, sources say, the scenario for the summit wasn't written solely for its potential domestic political effects. It also was intended to demonstrate to the visiting government heads Carter's desire to give Washington's long-neglected relations with Latin America a new measure of high-priority attention.

In the seven months since he took office, Carter has devoted more attention to this effort than any President since John F. Kennedy and his Alliance for Progress of the early 1960s. To launch the effort, he sent his wife, Rosalynn, Secretary of State Cyrus R. Vance, U.N. Ambassador Andrew Young and a flock of other officials on highly publicized tours of the region.

Now, in the events unfolding here this week, he has taken the process a step further - partly by presenting the canal treaties as a U.S. effort to promote relations with Latin America and partly by his marathon round of private, face-to-face meetings with each of his visiting opposite numbers.

In fact, administration sources insisted yesterday, these meetings are regarded at the White House and State Department as the most significant part of the "Week of Panama."

Carter, they said took special care to brief himself on every major outstanding issue between Washington and his visitors' countries, regardless of their size. His intention the sources added, is to listen to his visitors' complaints, to inform them of Washington's attitude towards events in their countries and to use these exchanges as the springboard for future effects at better bilateral and regional cooperation.

However, as was made clear by yesterday's bombings, exile demonstrations and other signs of protest, Carter's ambitious hopes of drawing his visitors together in one hemispheric happy family isn't something that can be accomplished within the framework of simple ceremonial get-together.

The principal problem is the ideological one that divides the region between dictatorships and democracies. Of the 24 governments that sent their leaders or other representatives here, 13 - including that of Carter's treaty co-signers. Torrijos - are non-democratic regimes whose methods of governing include considerable repression of their citizens.

For that reason, most of yesterday's demonstrations were focused on charges that Carter, by personally receiving dictators or their representatives at the White House, has betrayed his own devotion to the promotion of human rights and has given these regimes a stamp of respectability.

These charges were rejected by administration spokesmen who countered that the President believes he can do more for the cause of human rights in Latin America by using persuasion and frank talk on the region's leaders than by ignoring them.

In the case of every country where a human rights problem exists, the sources said, Carter was fully briefed on the details and brought them up in his talks with that nation's visiting representative.

Since some of the meetings have not yet taken place, the sources said it is too early to attempt to draw up a balance sheet on what the meetings may have produced. In addition, they added, the President has not had time to inform other administration officials in any detail of what is being said in the meetings.

But, they insisted, the sensitive topic of human rights was discussed in every applicable meeting, with Carter making clear in forceful terms that it is a subject to which the United States attaches extreme importance.

Although he was careful to avoid specifics, Carter acknowledged the presence of human-rights questions in the discussions during a brief exchange with reporters following his meeting Tuesday night with Chile's President Augusto Pinochet Ugarte.

Pinochet is the most controversial of the visiting governmental heads, because of the reputation of his regime for widespread murder, torture and imprisonment of Chilean political dissidents. Asked if he had discussed these charges with Pinochet, Carter replied that the Chilean leader is aware that his government does not have a very good reputation in the international community.

In a separate meeting with the press, Pinochet confirmed that Carter had discussed the Chilean human rights situation with him, and that he had told the U.S. President that, although it had been necessary to temporarily deny some rights following his government's rise to power in a 1973 military coup, the situation within Chile is now improving rapidly.