July 7, 1984

President Reagan, in an interview made public today, expressed doubts about future financing of Social Security. Mr. Reagan said in the television interview, filmed Monday, that he would never ''pull the rug out'' from under those now receiving Social Security benefits. But he said, ''There is a possibility - well, probability - that many people, young people now paying in, will never be able to receive as much as they're paying.'' He suggested that that was unfair.

Bicycle messengers, who have been accused of recklessness by city lawmakers, will be regulated for the first time under a bill signed yesterday by Mayor Koch. The measure was drafted after complaints to city officials that the cyclists endangered pedestrians, drivers and themselves by ignoring traffic laws. The new law requires commercial cyclists - those who deliver everything from groceries to legal briefs - to carry identification cards and to display their employers' names on vests, jackets or similar clothing. It also requires the employers to keep log books of where their cyclists go and when.

Text of statement, page 5. MOSCOW, July 6 - The Soviet Union today reiterated its offer to hold talks with the United States on banning arms in space, but appeared to add a precondition, calling for a mutual moratorium on testing. A Government spokesman said that such talks, which the Soviet Union has proposed for September, would be ''incompatible'' with the continued testing of space weapons. The spokesman's comments came at a news conference here after Tass, the official press agency, issued a new statement saying that Moscow's offer for negotiations to ban all types of weapons in space remained open.

The nation's unemployment rate fell by four- tenths of a percentage point in June, to 7.0 percent, the lowest level in more than four years, the Labor Department reported today. The June decline, the second consecutive large monthly drop in unemployment, was well distributed among all categories of workers: adults and teen- agers, men and women, and white, black and Hispanic people. Gains in Employment Coupled with a solid June gain in employment, the reduction in joblessness suggested that the economy continued to expand at a strong pace in June, a stronger one than the Reagan Administration expected. ''I would worry if it doesn't slow down further in the third quarter and fourth quarter,'' said Martin S. Feldstein, chairman of the Council of Economic Advisers. He was alluding to the possibility that the rising level of economic activity might cause inflation to acclerate.

Modern Israel, now 36 years old, is moving from the generation of its founding into the generation of its maturity without having resolved the most fundamental questions faced since its creation. In essence, they are the issues of what kind of a society this will be: religious or secular, nationalistic or humanistic, Western or Middle Eastern, absolutist or pluralistic. The struggles between these diverse qualities are intense; they are determining the nature of democracy and Judaism, the two key elements of Israel's fate. The writer of this dispatch has just completed a five-year assignment as bureau chief of The New York Times in Jerusalem. Some social thinkers believe that clear resolution of the conflicts is impossible and perhaps not even desirable because the varied population of Jews from throughout the world has remained intact partly because of the society's ambivalence. Its ability to sustain tension between opposing impulses has made room for variety. If the state became unequivocally religious, for example, the secular Jews would be alien, and if it became wholly secular, the religious would feel apart.