President Reagan's job performance rating has dropped sharply, with 59 percent now approving of Reagan's handling of his presidential duties, 28 percent disapproving and 13 percent undecided.

For two months after the March 30 attempt on his life, Reagan enjoyed the confidence of two-thirds of the American people for his handling of his presidential duties. The latest Gallup Poll, however, shows a 9 percentage point decrease from a mid-May survey, when his positive rating stood at 68 percent.

This decline in approval is nearly matched by a seven-point increase in those who disapprove of the president's job performance, from 21 to 28 percent -- the highest level of disapproval noted during Reagan's brief tenure and higher than that recorded for any other president at this point in his administration.

By way of contrast, Presidents Carter and Nixon not only had slightly higher approval ratings at similar points in 1977 and 1969, respectively, but significantly fewer people disapproved of their stewardship.

Analysis of the intensity with which the public holds its views of Reagan's job performance shows that about half of those who approve do so "very strongly" and the other half "not so strongly." Conversely, strong disapproval outweights moderate disapproval by a 3-to-2 ratio. This pattern of disapproval is unlike that usually found in these measurements, in which moderate exceeds strong disapproval.

Recent Gallup surveys showed Reagan to be personally more popular than his handling of specific problems. The current study, however, suggests that concern over the cuts in social programs, dissatisfaction with the proposed reductions in Social Security benefits and criticism of the tax cuts are now being reflected in the president's lower overall performance ratings.

Although the Reagan economic and Social Security proposals have been seen by some to have a disproportionate effect on the less-advantaged segments of the population and the elderly, the president's decline in popularity has occurred about equally in all demographic groups.

For example, compared to a nationwide decline of nine percentage points since the previous survey, Reagan lost six points among Americans under 30 years old, 10 points among 30-49-year-olds and nine points among those over 50. Similarly, the president's popularity fell by eight points among individuals whose family income is $15,000 or more and by nine points among those with family incomes of less than $15,000.

Reagan suffered a loss of popularity not only among Democrats (off seven points), but also Republicans (down five) and independents (down 12) as well.

The latest results are based on 1,515 personal interviews with adults, 18 and older, conducted in more than 300 scientifically selected locations across the nation during the period June 5-8.

For results based on a sample of this size, one can say with 95 percent confidence that the error attributable to sampling and other random effects could be three percentage points in either direction.