President Reagan directed NASA Administrator James C. Fletcher yesterday to implement the Rogers commission's recommendations on the space shuttle disaster "as soon as possible" and to report back in 30 days with a plan for doing so.

"The procedural and organizational changes suggested in the report will be essential to resuming effective and effi- cient Space Transportation System operations and will be crucial in restoring U.S. space launch activities to full operational status," the president said in a letter to Fletcher.

Reagan called on Fletcher to include in his 30-day progress report "milestones by which progress in the implementation process can be measured."

The NASA chief met briefly with Reagan at the White House to receive his marching orders but declined to comment on the private exchange.

Shirley Green, a spokeswoman for Fletcher, said he assured the president of his best efforts to "return NASA to its high levels of excellence."

She would not deny that the two discussed NASA's push for approval of an extra $1.9 billion or more in federal funds to buy a replacement for Challenger, but she declined to comment on what they said about it.

The subject has produced confused signals from the White House. Reagan said in a nationally televised news conference Wednesday night that he thinks "we should go forward with another shuttle." But top administration officials have expressed serious reservations about whether building a fourth orbiter is justified.

White House spokesman Larry Speakes said yesterday that while Reagan's "inclination" is to approve the fourth orbiter, it is part of a broader decision on the shape of the nation's space program. That decision could come in the next several days, he added.

Fletcher, a former NASA chief who was appointed again in the accident's aftermath, endorsed the commission's findings earlier this week.

Some experts predict that compliance with all the recommendations will mean soaring costs and delay of the next shuttle flight until at least early 1988. The National Aeronautics and Space Administration has set July 1987 as a tentative target date for the next launch.

The report called for drastic changes in the structure of shuttle management, a greatly strengthened safety program, improved communications, reduced pressure on the shuttle launch schedule, safety improvements in shuttle landings and a more rigorous hardware maintenance program.