The Carter administration, over the objection of its key inflation-fighting agency, has agreed to permit unions to "front-load" their wage settlements to provide pay increases of up to 10 1/2 percent in the first year of the contract.

The decision, announced yesterday, was made by the president's Cabinet-level Economic Policy Group at the urging of the tripartite Pay Advisory Committee. The Council on Wage and Price Stability had protested the move as inflationary.

The action marked another setback for the wage-price council, which has lost several major disputes with the pay committee over the past several months. The pay panel is headed by former Labor secretary John T. Dunlop.

The shift would allow unions to skew their settlements to provide pay hikes of up to 10 1/2 percent in any year of a multiyear contract as long as the increase over the life of the pact amounts to a yearly average of no more than between 7 1/2 percent to 9 1/2 percent.

Until yesterday, the administration's guidelines had asked unions to keep their settlements within the 7 1/2 percent-9 1/2 percent range during each year of a contract's lifetime -- without any front-loading.

Front-loading a contract permits union workers to get more money over the life of their contract agreement even though the overall percentage figures are in compliance with the government's guidelines.

The Dunlop panel had contended that unions needed more flexibility in their contract negotiations than the 7 1/2-percent-9 1/2 percent limit provided, and insisted it never intended to bar front-loading when it drafted the new rules last fall.

R. Robert Russell, director of the wage-price council, had argued that the more liberal interpretation would invite higher wage settlements this year and intensify inflation's momentum. However, he was overruled.

The announcement came as the government reported that new factory orders for durable goods, a key indicator of the strength of the economy, plunged 7.3 percent in May -- the sharpest monthly drop since December, 1974.

Meanwhile, four of the nation's largest banks lowered their prime lending rates by half a percentage point to 12 percent, completing the industrywide move to a 12 percent prime rate that began more than a week ago.

The May plunge in durable goods orders, the fourth monthly decline in a row, sent overall factory orders for durable goods plummeting $5.34 billion to a new level of $66.95 billion.

The 7.3 percent drop for May followed declines of 6.9 percent in April and 4.3 percent in March. The combination marked the steepest plunge since the 1974-75 recession, which was the worst since the late 1930s.

Particularly discouraging to some analysts was the steep plunge in new orders for nondefense capital goods, which plummeted 10.8 percent in May, following decreases of 1.9 percent in April and 5.2 percent in March.

However, the Commerce Department said the bulk of the decline came in new orders for aircraft, a particularly volatile sector, where ordrs fell 23 percent, or $4 billion in a single month.

Excluding the aircraft and transportation sector, new orders fell only 2.4 percent. Shipments by durable goods manufacturers fell 4 percent, or $2.9 billion, mostly in the beleaguered auto and steel industries.

However, despite this falloff, overall shipments still exceeded new orders, resulting in the first reduction in the backlog of new orders since August 1976 -- and possibly paving the way for production increases later.

The cut in the prime rate was the latest in a series of reductions in the prime since the recession began to take hold last April. The prime is the interest rate that banks charge their most creditworthy corporate customers.

Separately, officials disclosed that wage-price council director Russell plans to continue in his post at least through the November election. Earlier, there had been speculation that Russell was about to be ousted over policy differences.