President Carter formally endorsed a full employment bill yesterday that would establish a national goal of 4 per cent unemployment within five years but would not require the administration to take specific steps to reach that percentage.

The President's long-awaited endoresement of the so-called Humphrey-Hawkins bill came after weeks of intensive negotiations with congressional supporters of the legislation, and a growing [WORD ILLEGIBLE] of charges that Carter has not fulfilled campaign promises to aid blacks and the unemployed.

However, the new bill appeared to be such a watered - down version of the original that even a White House aide wondered aloud why the bill's supporters accepted it.

The bill would require tha President annually to establish goals of employment, the unemployment rate, production and other economic factors for each of the next five years. It would mandate that the initial five-year goal on unemployment - to be reached by 1983, should the legislation be passed in 1978 - be an overall unemployment rate of 4 per cent of 3 per cent or less for adults aged 20 and older.

However, in another section of the measure, the President would be empowered to alter the 4 per cent unemployment goal, raising the target to a higher rate if he thought that necessary. He would be empowered to modify the goal three years after the measure was enacted - in 1981 should the bill pass next year.

In effect. the measure, if enacted next year, would mandate a 4 per cent unemployment goal through the 1980 presidential election, after which it could be modified.

The bill also contains a section, inserted at White House insistence, setting-forth possible policies to combat inflation. But as in the sections dealing with unemployment, nothing in the legislation would require the administration to take anti-inflation steps.

Reports were briefed on the compromise version of the legislation yesterday by three high-ranking administration officials under ground rules that did not allow them to be quoted by name. Under questioning, one of the officials, a Cabinet secretary, conceded that the bill "doesn't in itself do anything."

In keeping with recent administration efforts to calm business fears over increased government spending and a possible new round of inflation, the officials also stressed that the legislation "does not authorize new programs or add money to the federal budget."

But they argued that establishing a national goal on unemployment is important in itself so long as the President retains "flexibility" in seeking to reach the goal.

"It is a desirable goal, but one that will be very difficult to achieve," one of the officials said.

Unemployment nationally is currently 7 per cent. Carter has established his own goal of reducing unemployment to 4.75 per cent by 1981.

The President first endorsed the concept of the legislation last year during his campaign, although he never appeared to be an enthusiastic backer of it. Earlier versions of the legislation would not only have established an unemployment goal but also would have required specific steps to reach it.