WASHINGTON, Feb. 20— The Presidential commission investigating the space shuttle explosion is increasingly focusing on whether top managers of NASA's Marshall Space Flight Center pressured the manufacturer of the Challenger's booster rockets to approve the launching, sources close to the panel said today.

At a news conference this morning, Jesse W. Moore, the space agency official who gave final approval for the launching, reiterated that he had never been informed of a near-rebellion among the manufacturers' engineers fearful that a launching would lead to disaster.

The explosion, 73 seconds into liftoff, killed the seven astronauts on board. New Executive Is Named

As expected, Mr. Moore announced he was relinquishing his position as associate administrator in charge of the shuttle project while remaining head of the Johnson Space Center in Houston. Rear. Adm. Richard H. Truly of the Navy is to replace him. [ Page A12. ] Tonight, the National Aeronautics and Space Administration released the document it received from the booster manufacturer the night before the Jan. 28 launching giving final authorization to proceed. Signed by Joseph C. Kilminster, Morton Thiokol Inc.'s vice president for space booster programs, the one-page assessment warned that the O rings sealing critical joints on the booster would harden in the cold and thus take longer to ''seat'' properly, but concludeed with a statement that Morton Thiokol ''recommends STS-51L launch proceed on 28 January 1986.''

At the news conference earlier today, Mr. Moore said: ''Whether or not this decision or this issue stopped at the Marshall Space Flight Center I'm not prepared to comment on, quite honestly. I have not actually sat in front of someone and gotten that specific piece of information.'' Panel Members at Marshall

Two commission members, Neil Armstrong, the former astronaut, and Brig. Gen. Donald Kutyna spent today at the Marshall center in Huntsville, Ala., interviewing officials there with an eye toward bringing them to Washington for public hearings next week.

So far, much of the investigation into the launching decision has centered on a second-tier official, Lawrence B. Mulloy, the head of the solid-fuel booster rocket project at Marshall. According to several reports, Mr. Mulloy argued heatedly with Thiokol engineers when they said, the night before the launching, that it was too cold to attempt a launching.

But investigation sources say they are now trying to determine who else was involved in these discussions, and NASA officials said they did not know where the investigation would stop.

The document made public by NASA tonight does not reflect what Thiokol engineers say was a near-unanimous consensus against launching. But it does caution NASA officials that the O rings would be 20 degrees colder than on a January 1985 shuttle flight. That flight resulted in severe erosion of the primary rings on the shuttle boosters. NASA had previously said the temperature of the rings at the time of the last launching was about 30 degrees. Likened to January 1985 Flight

The bottom line, the Thiokol document concluded, was that the Challenger flight ''will not be significantly different'' from the January 1985 flight. A notation on the document indicates that it was sent both to the Kennedy Space Center at Cape Canaveral and to Marshall.

Experts who have examined photographs made public by NASA last week say, however, that a puff of black smoke that appeared immediately after launching may indicate that the seals began to burn through immediately. But they have not ruled out other causes.

The new turn in the investigation came as the question of who overruled the engineers' warnings, and why they did so, deepened. Investigators said it was becoming urgent to discover how high up in NASA the question of the effects of cold on the booster rockets' rings was discussed in the hours before the launching.

Investigators are still mystified, several sources say, by the critical sequence of events the night before the launching, when NASA officials and Thiokol engineers held a telephone conference on whether to proceed.

According to all accounts, Thiokol's first recommendation, based on the potential effects of the cold on the booster seals, was not to try a launching below 53 degrees. The predicted temperature for the launching the next morning was in the mid-30's, and the nighttime temperature was dropping well below freezing at Cape Canaveral, even as the conference wore on. Crucial Conference

''At some point after that recommendation, someone called a five-minute break,'' said the source, who insisted on anonymity. But the recess stretched more than half an hour, the source said, and when it resumed, top Thiokol managers reversed themselves and approved the launching.

Both investigators and engineers at the company say they do not know what led to the reversal. A company spokesman has said that the reversal came ''after considering some additional information,'' but the information itself has never been specified.

One engineer who spoke on the condition that he not be identified said he did not know why the decision was reversed, but added, ''Nobody wants to be the one that says 'No' '' to liftoff. The mission had already been delayed three days, and some engineers have said that pressure to launch the shuttle was building.

Just where the pressure, if any, was coming from, however, is still not clear. The NASA officials arguing for a launching were reportedly Mr. Mulloy at the Cape and Stanley Reinartz, the manager of the shuttle projects office at Marshall. Neither responded to telephone calls today. The officials would not say what role the director of Marshall, William R. Lucas, had played, if any. Marshall's Responsibility

Marshall is only one of the NASA groups that would have played a role in the decision, but it was probably the most important. It is responsible for the overall design of the propulsion systems that send the shuttles into orbit. The orbiter itself, in contrast, is the responsiblity of the Johnson Space Center, and the launching and shuttle processing operations fall under Kennedy Space Center.

Any of the three units could have stopped the launching, but it appears that only Thiokol communicated with Marshall officials, because they have primary responsibility for the booster rockets.

In the end, Thiokol engineers say, it was Mr. Kilminster, a top official at Thiokol's Wasatch division near Brigham City, Utah, who gave the go-ahead to NASA, over the continued objections of other engineers. One of them, Allan J. McDonald, the director of the solid-fuel rocket motor project at Thiokol and the company's top official at Kennedy, has said he continued to argue against the launching well into the night.

Democrats on a Senate panel investigating the launching had hoped to hold a private meeting with Mr. McDonald in Washington today, but when he and other Thiokol employees learned that reporters knew of the meeting, they decided not to appear. Instead Mr. McDonald spoke to the senators briefly by telephone.

photo of letter (page A12); photo of Rear Adm. Truly