The Reagan administration yesteday began the delicate task of moving ahead with its planned sale of sophisticated additional equipment for Saudi Arabia's F15 jet fighters, while reassuring Congress it will take steps to ensure that Israel's security is not threatened by the increased Saudi air power.

Although the State Department continued to insist that "no decisions have been made" about the Saudi requests, it now is certain that the administration intends to meet that vital oil-producing state's demand for extra-large fuel tanks and bomb racks that will increase the range and firepower of the 62 F15s it has ordered from the United States.

At closed meetings yesterday with the foreign relations committees of the House and Senate, the new undersecretary of state for security assistance, James Buckley, laid out the administration's proposals. They call for softening Israeli opposition to the Saudi sale by offering Israel increases in its F15 fleet.

Specifically, the administration, in proposals discussed here earlier this week with Israeli Foreign Minister Yitzhak Shamir, intends to allow Israel to purchase 10 F15s, in addition to the 40 the United States already is committed to sell, with a 10-year grace period before repayment would begin.

In addition, the administration is expected to offer Israel some help repayment of loans to ease the pressures on the troubled Israeli economy. The United States also is expected to permit the Use of American-made components in Kfir jets that Israel wants to sell to Third World countries and to give Israel "enhanced early-warning capability" to guard against the possibility that the Saudi jets might be used against it.

It was not immediately clear what this "enhanced" capability will involve. Even if the United States was willing to grant them, Israel cannot afford the ultra-sophisticated airborn warning and control SYSTEM (AWACS) planes, and it is likely that the United States will offer more modest help.

Although Israel publicly is on record as opposing the Saudi sale, the administration's plans for a compromise are know to originate in Israeli signals that if the United States is determined to go ahead, Israel should be compensated in ways that will help it counter any possible threats from the Saudi planes. Spurring Israel's flexibility is the knowledge that the turn back any attempt by Israeli supporters in Congress to block the sale.

However, congressional sources said, Israel is somewhat disappointed by what it regards as a relatively limited and inadequate U.S. compensation offer. For one thing, the administration apparently plans to offer the additional 10 jets ar regular 12 percent financing rather than the special lower-interest rate Israel had hoped for. However, the sources said, the administration is prepared to let Congress set terms more to Israel's liking.