The escalating and intractable Iranian hostage crisis provoked new confusion and anxiety yesterday after claiming the American secretary of state as its latest victim.

A stunned nation's capital witnessed the formal resignation of Cyrus R. Vance, the first secretary of state to give up his office on a point of principle since 1915. Vance's decision to quit jolted the Carter administration, intensifying the president's political problems.

Americans had to digest this startling news at the same time that they struggled with nauseating pictures on their living room television screens -- images of Iranians toying with the incinerated corpses of American servicemen.

In Texas yesterday, President Carter, who has refused to leave the White House to campaign for reelection, appeared beside the hospital beds of five injured servicemen, the survivors of last week's failed attempt to free American hostages in Tehran. "I'm overwhelmed with emotion," Carter said.

Politicians of many different persuasions spoke highly of Cyrus Vance yesterday, many voicing concern at his resignation. In private comments, prominent figures expressed deep dismay at another sign of confusion and uncertainty in the country's foreign policy.

"Considerable disarray," said Sen. Jacob K. Javits (R-N.Y.). Both the Senate Foreign Relations and the Armed Services committees plan to hold hearings.

Abroad, reactions were strong. Comments from many lands suggested that foreigners see Vance's departure as new evidence that America under Carter is confused and erratic.

The Soviet Union concluded that hard-line elements have taken control of American diplomacy. And America's European allies decided to apply new, coordinated pressure on the Carter administration to try to head off any further military action against Iran.

In Tehran, the Revolutional Council voted to turn over the remains of the eight Americans killed in the aborted raid to representatives of Pope John Paul II and the Red Cross.

Vance's resignation, it seemed, instantly legitimized criticism of the aborted American rescue operation -- criticism that might have seemed harsh or tasteless just the day before. If the secretary of state resigned over the issue, it was now possible for others to speak up openly with their criticisms.

For all the drama of this extraordinary Monday in April, none of it seemed to add up. A bold American initiative had ended in failure and humiliation, and the only resulting resignation came from the one senior official who had opposed the plan. Secretary of State Vance said he had resigned on principle, but he failed to explain just what the principle was.

The fury provoked by the desecration of American corpses in Tehran may add to public frustrations and pressures for another round of military action against Iran, though new military moves could also deeply divide the country. Sources high in the Carter administration said they think the president is still on a course that would lead to further military moves sometime this spring or summer.

In the friendly handwritten letters exchanged by Vance and Carter and released yesterday, the secretary's misgivings were disguised behind curt phaseology. "I know how deeply you have pondered your decision on Iran," Vance wrote to the president. "I wish I could support you in it. But for the reasons we have discussed, I cannot."

Vance's reasons, it was learned, were direct -- and directly contradictory to the president's reasoning. Vance thought the use of military force to try to free the hostages would only exacerbate the crisis and would create grave new dangers in the Persian Gulf.

Before Carter approved the rescue plan April 11, Vance had told the president in considerable detail of his reasons for opposing the effort, and had informed the president that he would resign if it were carried out, according to presidential press secretary Jody Powell.

"The president remained singularly unpersuaded [by Vance's arguments]," Powell said. "The president went ahead with it knowing whether it was successful or not, it would cost him a secretary of state."

The White House said yesterday it hoped to select a successor to Vance quickly. The front-runner appeared to be Warren M. Christopher, Vance's deputy secretary. Vance endorsed Christopher at a private meeting with his principal aides at the State Department yesterday. But even Christopher himself, sources said, has no idea if he will get the job.

All of Vance's aides will stay on at least temporarily, and most of them appear willing to finish out the administration's term, provided the new secretary is congenial. Vance asked them all to support the president and stay on the job.

Powell told reporters yesterday that the president regretted Vance's departure but had come to understand that it was inevitable. "A lot of us had a great deal of respect and a significant amount of affection for him." Powell praised Vance's handling of the episode: "He handled it considerably better than Dick Clark," Powell said, a tart reference to the former senator who quit a State Department refugee job to join the campaign of Sen. Edward M. Kennedy.

A number of the president's assistants expressed their own apprehension over events. "My first reaction when I heard that Vance had quit was, 'Does this mean that I should too?'" said one mid-level White House assistant. "I wondered what there was that he knew that I didn't know."

Instead, this aide and others say, they saw the members of the White House inner circle of senior assistants appearing confident and in control. "There was no sign of panic, no altered behavior," one assistant said. And there were no discussions of any similar resignations of conscience from the White House staff, he said.

While the president's senior staff was being briefed on the resignation of Vance, the president was meeting with Vance just down the corridor. The farewell session between the president and the man who had served him as secretary of state began at 9 a.m.

An hour and a half later, the president left the White House, ending his self-imposed travel ban, and flew to Texas to visit with five of the men who were burned or otherwise injured in the crash that followed his order to abort the rescue mission in Iran.

His face grim, the president walked past cheering crowds at the Lackland Air Force Base medical facility. After donning surgical gear and greeting the men, Carter praised Vance for his dedication.

Carter was asked whether Vance's resignation would hamper future negotiations with Iran. The president replied in terms of military action, rather than diplomacy.

"His departure did not have any adverse effect upon the rescue of American hostages, nor will it in the future," Carter said.

In London yesterday, former president Richard M. Nixon told a television interviewer that he had not expected Vance to resign. "It surprises me that Mr. Vance would resign over that," Nixon said, "because he has been such a good soldier."