At least $350 million will be needed this year and next to correct the space shuttle's solid rocket booster problems and to make other system modifications resulting from reviews of the Challenger disaster, William R. Graham, the space agency's acting administrator, told a congressional committee yesterday.

It was the first time since the Jan. 28 shuttle explosion that an official of the National Aeronautics and Space Administration has conceded that a redesign of the booster joints and seals is necessary.

Graham also said the space agency is estimating a year's delay before a shuttle flies again and is studying whether its launch schedules have been too ambitious.

Design defects in the joints that connect the booster segments and the O-ring seals that keep the booster's hot gases from leaking are thought to be a leading cause of the explosion that took the lives of Challenger's seven crew members.

"My view today," Graham said, "is that it would be very appropriate to modify or redesign the seal rings."

In another development yesterday, it was revealed that the chief of the astronaut program, John W. Young, warned in an internal memo two months ago that the space agency was risking a potentially catastrophic landing accident because of its "political policy" of landing shuttles at Kennedy Space Center in Florida rather than Edwards Air Force Base in California.

Graham, making his first budgetary presentation to Congress since the accident that destroyed the $3.2 billion shuttle, told the House Science and Technology Committee that the administration has yet to decide whether to seek funds for a new orbiter.

Graham put the cost of a new shuttle at $2.8 billion and said it could be ready to fly 3 1/2 to 4 years after it was authorized. He made it clear that he believes a fourth orbiter is needed and received support for that position from committee members.

Graham said that without the fourth shuttle, there would be a backlog of 24 full shuttle loads by 1990, which "would grow [in succeeding years] with no cost-effective way to reduce it."

To illustrate his current problem in dealing with commercial customers, Graham said that last Friday he had to tell the British, who wanted their Skynet satellite carried into orbit in 1989 or 1990, that "the United States was interested but not able to commit a reliable launch capability in view of the backlog."

That response drew a strong protest from Rep. Bill Nelson (D-Fla.), chairman of the panel's space subcommittee and a passenger on the shuttle flight before Challenger. The committee, Nelson said, "feels unanimously that it doesn't want to see commercial payloads given up."

Graham said NASA's planning has focused on a 12-month delay as the most reasonable, recognizing that much depends on the report of the presidential investigating commission headed by former secretary of state William P. Rogers.

Responding to a question about chief astronaut Young's suggestion in a separate memo last week that the pressures of the launch schedule may have contributed to the accident, Graham told the committee that NASA "is conducting a complete review of the launch rate issue."

Graham said that when flights start again, there would be a three-month wait between the first and second flight and then at least a two-month wait until the third flight.

NASA "intends to resume at a fairly low rate," he said. "We don't intend to increase until the launch rate is safe and appropriate to the system."

The slow return of shuttle flights would affect NASA's two major space probes, the Ulysses vehicle to explore the sun's poles, and Galileo, which is to investigate Jupiter. Graham said the agency, which once planned to launch those two ambitious experiments this May within 15 days of each other, now will have to choose between the two for a mission in June 1987.

Chief astronaut Young, in a strongly worded Jan. 6 memo on landing problems, contended that the Kennedy Space Center posed serious safety hazards -- including a narrow, inadequate runway and unpredictable weather -- that carry "a significantly higher probability of costing NASA orbiters and killing flight crews."

As part of its overall goal of increasing the number of shuttle launches, NASA had recently adopted a policy of landing orbiters at Kennedy in Florida rather than at Edwards to spare the five days it takes to ship the orbiter back from California for its next mission.

But Young said he "urgently recommended" that shuttle landings return to Edwards because the technical problems of landing at Kennedy "cannot be solved in our environment of limited resources."

The memo was addressed to George W.S. Abbey, chief of crew operations at Johnson Space Center in Houston, three weeks before the Challenger explosion. Challenger was scheduled to be the first shuttle to land at Kennedy since April 1985.

A copy of the Young memo appeared in yesterday's Houston Post and was released by NASA later. NASA spokesman Hugh Harris declined comment on the memo.