For the second time in just a few days, one of the nation's leading polling organizations is reporting a decline in the popularity of President Reagan.

According to the findings of a new Louis Harris poll, 60 percent of the public gives the president a favorable rating and 39 percent a negative rating, down from 67 percent positive and 29 percent negative in a Harris poll in April.

"On overall estimates and on his own personal performance, the president stands very high indeed," Harris said. "But on specifics, especially those related to his key domestic and foreign policy stands, has ratings have dropped since late April, with many of them now on the negative side."

According to the poll, in which 1,245 people were interviewed by telephone from June 3 to 7, a 51 to 47 majority gives Reagan positive marks for his handling of the economy, down from a 58 to 36 positive rating five weeks earlier. Reagan gets a 56 to 41 percent negative rating, however, on his performance in "getting inflation under control."

In addition, by 68 to 30 percent, a majority rates Reagan negatively on "caring for the poor, the elderly and the handicapped," according to Harris.

In one area, "handling relations with Congress," Reagan is given a highly positive rating of 66-31. And on the question of "inspiring confidence in the White House, a 68-30 majority regards Reagan positively. In both areas, though, Reagan scored higher in the April Harris poll.

In addition, Harris notes that Reagan gets "barely positive marks" for his handling of foreign policy and a negative score for "appointments to important positions in his administration."

On Sunday, the Gallup Poll reported what it referred to as a sharp drop in Reagan's job performance rating in early June, with 59 percent saying they approved of his handling of the presidency and 28 percent saying they disapproved. The previous Gallup Poll, taken in May, had 68 percent saying they approved with 21 percent disapproving.