For the second time in two weeks, the actions of Sectary of State Alexander M. Haig Jr. have prompted questions inside and outside the Reagan administration about the way he is conducting himself in office.

Haig's latest problems stem from his performance in the aftermath of the assassination attempt on President Reagan -- first with his shaky, emotional claim over national television of constitutional authority in the line of presidential succession, and then through a private disagreement in the White House Situation Room with Secretary of Defense Caspar W. Weinberger.

The dispute, according to a source, centered on Weinberger's displeasure with Haig's televised remarks and disagreement over the nature of the increased readiness procedures that were ordered for U.S. miliary forces around the world.

As the controversy became a matter of public discussion yesterday, senior White House assistants moved with swiftness to praise Haig and minimize the political damage. Last week, Haig was critcized by Reagan aides for his open disagreement with the president's plan to name Vice President Bush to direct White House crisis management.

Yesterday, top presidential assistants lauded Haig's performance in the Situation Room during those hours Monday in which Reagan was on the operating table and Bush was in an airplane, returning to Washington. "I worked at his side in the Situation Room from 2:30 to 8:30," said White House staff director David Gergen, "and he was steady, very steady. He did a hell of a job."

Presidential aides also minimized the nature of the disagreements between Haig and Weinberger, conceding that there were some disagreements -- some "sparks," as one called it -- but emphasizing that there was never a boisterous "row" between the two Reagan Cabinet members.

Spokesman at the departments of State and Defense also moved rapidly yesterday to deny that there was any rift between Haig and Weinberger. "Everything went smoothly," said Army Maj. Gen. Jerry Curry, the Pentagon spokesman. "There was no argument between Haig and Weinberger, nor were there heated words or heated exchanges that would involve conflict between the two."

Meanwhile, back at the White House, even those officials most anxious to praise and support Haig would not go quite that far in their denials."There were some disagreements," said one senior presidential assistant," . . . some disagreements between Haig and Weinberger. But the so-called set-to between Haig and Weinberger has been exaggerated."

Whatever the details of disagreements in the Situation Room, Haig's appearance on television from the White House press room raised eyebrows among officials in the State Department, Pentagon, White House and on Capitol Hill who, like Americans everywhere, were glued to their TV sets watching the day's events unfold.

One State official, who said Haig was cool and collected when he left for the White House shortly after the shooting, was stunned by what he saw on television little more than an hour later when Haig was at the White House lecturn.

Haig was perspiring heavily. His voice appeared to be cracking, rising and falling unsteadily and his arms seemed to be trembling. "I've never seen him like that before and I've known him for many, many years," the official said. "He was cracking emotionally. We were all worried about the president and didn't know if it was a plot. He [meaning Haig] went through an assassination attempt himself in Belgium."

In June 1979, just before he left his post as the four-star general in command of NATO troops, Haig narrowly escaped an apparent attempt on his life when a bomb was set off under a bridge just as Haig's car was crossing.

Four days, later, accounts of his farewell news conference reported him as seeming "somewhat emotional and combative," descriptions that were heard again yesterday.

What Haig said added to the concern throughout government.

Asked who was making the decisions for the government, Haig said: "Constitutionally, gentlemen, you have the president, the vice president and the secretary of state in that order and should the president decide he wants to transfer the helm to the vice president, he will do so. He has not done that. As of now, I am in control here, in the White House, pending return of the vice president and in close touch with him. If something came up, I would check with him, of course."

At the State Department, officials said Haig was talking about the precedence of the secretary in the Cabinet and his position, in that role, of being in charge of the Situation Room at the White House during that short period while Bush was still out of town.

Officials at the Pentagon, however, pointed out privately that Haig was wrong on two counts in what he said and that the way this came across to the public was that he was running the country.

It has now been pointed out by the White House that the secretary is fifth in line in terms of succession to the presidency, according to the Constitution, and that the national command authority, with respect to the president's role as commander-in-chief of the armed forces, goes from the president, to the vice president to the secretary of defense.

In fact, Haig's statement about being in control in the Situation Room was technically accurate. As soon as Haig learned that Reagan had been shot, he called White House chief of staff James A. Baker III and, according to Baker, suggested that he, Haig, should be in charge of decision-making in the Situation Room.

Baker diplomatically referred to Haig being the "point of contact" among the Cabinet members in the Situation Room.

While in the Situation Room, Haig and others present listened to deputy press secretary Larry Speakes conduct a briefing for reporters. At one point, Speakes said he could not answer a question about whether U.S forces had been put on alert status in the wake of the shooting of the president.

Haig then decided, on his own, according to White House officials, to go to the press room and make himself available for questions in order to reassure allies.

It was there that Haig made his now-controversial television appearance. Later, back in the Situation Room, Weinberger let Haig know that he was upset with the Secretary of state's characterization of himself as being No 3. in line of authority, according to several sources.

After that, Haig and Weinberger, were reported to have disagreed over the procedures for increasing the readiness status of U.S. military forces around the world.

"No extraordinary measures were taken -- we did not put our forces on 'alert,'" said one senior official. "But cautionary procedures were taken." The official did not elaborate.

But offering an insight into his dispute between the retired four-star general and the defense secretary, he added that the Secretary of defense, not state, has "the right a obligation" to make decisions of military command.

While one senior Pentagon official played down Haig's remarks, saying they amounted to just "a few mistaken words," another summed up the view of his colleagues about Haig's TV performance as "unbelievable. I just don't understand his demeanor," he added, "especially for one who says he's in charge."

Another senior official who knows and admires Haig said: "I don't know what to make of it. He's smart, experienced, able and handling himself badly. I just don't know how to put all that together. He's tense by nature, like a steel trap ready to spring, always on the edge of his chair," the official said as a possible explanation.

But, he added, Haig may be trying to do too much too fast, working too many hours while people around him may be pushing him too hard to reach out for areas that he shouldn't reach for.

"His big problem," the official said, "is that he doesn't understand the character of the president. He's an outsider trying to roll over the president's closed friends . . . and he is also a guy who is probably risking his life [Haig had major heart surgery a year ago], has given up a ten-million-dollar job and is unwilling to put up with nonsense."

On Capitol Hill, Haig's image problems were reflected by Rep. Barber B. Conable, a New York Republican, who said yesterday, "It looked to people up here like he go his foot in his mouth again and Bush performed well."

The relationship between Haig and the top Republican leadership on the Hill has been strained from the begining, other sources said yesterday.

The problem began in January when Haig was under attack during his confirmation hearings. It was learned yesterday that, after only two days of hearings, Haig called the new Senate majority leader, Howard H. Baker Jr. (R-Tenn), late at night to tell him that he, Haig, was withdrawing his name from consideration.

Baker, sources say, talked him out of the decision on grounds that, he would be letting the new president and new majority leader down and foreclosing other possibilities for himself later. The president and the Repulicans needed Haig, Baker said.

Now, however, as one top GOP congressional adviser puts it, there is a growing sense on Capitol Hill that Haig -- fairly or not -- is becoming a problem.