NASA officials yesterday announced that the next shuttle launch will be delayed another six months, at least until early 1988, because of unexpected difficulties with the redesign of the flawed solid rocket booster that caused the Challenger disaster.

The announcement, which could worsen the backlog of commercial, scientific and military payloads and mean more layoffs in the space program, came in a report to President Reagan yesterday outlining how the agency plans to implement the Rogers Commission's recommendations for overhauling the National Aeronautics and Space Administration and fixing booster problems.

Along with the report, according to a White House source, NASA Administrator James C. Fletcher handed the president a personal appeal for his support in building a fourth orbiter to replace Challenger, which disintegrated Jan. 28, killing its crew of seven. The White House has been unable to resolve the divisive question of how to pay for the proposed $2.8 billion spacecraft.

White House officials have said the decision is at least two weeks off.

At a news conference yesterday after he delivered the report, Fletcher said, "There is no guarantee when it's all done that there will be a fourth orbiter, because financing is a real problem."

Until yesterday, NASA officials had held to a target date of July 1987 for the next shuttle launch, although outside experts and some inside NASA had said that was overly optimistic.

"I guess we're all disappointed" about the schedule slip, Fletcher said, adding that the agency is being "a little conservative" and that "there are some that wanted to launch right away at a higher temperature." (Cold weather was found to be a contributing factor in the Challenger accident.)

"It's no fun to have to admit you're wrong in your assessments," said shuttle program chief Richard H. Truly. "But we'll fly just as quickly as we can." He said his teams "plan to work around the clock" in shifts.

Truly and Fletcher cited as the main reasons for the schedule change the need for "extensive testing," unexpectedly difficult tooling requirements for certain parts of the rocket boosters and unavailability of basic hardware.

The schedule slip means the U.S. space program will have been grounded for at least two years following the Challenger accident. It also increases the anxieties of space workers around the country about further layoffs in the embattled agency and among its contractors.

"We haven't got to that decision yet," Truly said, calling anxieties about layoffs at Johnson Space Flight Center in Texas "premature."

The agency's recent decision to move management of the space station from the Johnson Center in Houston to Washington headquarters means not only the loss to Houston of about 100 top management jobs, but that hundreds more planned job slots will not be opening there, officials said.

The agency's cancellation of the Shuttle-Centaur program, which was to lift science probes into deep space, also meant lost work.

The 50-page report to the president responded to Reagan's order last month that the agency implement the commission recommendations and supply within 30 days a blueprint for doing so.

Fletcher described it as "really a road map to get back flying again."

Most of the steps it outlined have been made public. Among them:

On the solid rocket booster redesign, analysis and testing of several design choices that involve minimum alterations of existing hardware are under way. In addition, a "totally new design which does not utilize existing hardware" will be developed in the event tests indicate none of the other design changes is good enough. An independent panel of experts from the National Research Council, an arm of the National Academy of Sciences, is monitoring the redesign.

Astronaut Robert Crippen has formed a group to assess shuttle management and communications problems and will report to Fletcher by Aug. 15.

All shuttle components considered critical to safety are being studied, with a final review scheduled for next March. The National Research Council will form an independent panel to monitor this effort as well.

Fletcher has formed a new NASA office to monitor safety and reliability throughout the agency.

A reassessment of escape methods for astronauts so far confirms that there is no effective means during certain portions of flight, but that methods for bailing out during a controlled glide are worth studying, along with other possible improvements. "We are a long way from concluding that that is worthwhile," Truly said.

Staff writer David Hoffman contributed to this report.