American businesses experienced a sharp pileup of inventories in April in the face of declining sales, but analysts said overall stockbuilding still wasn't excessive and didn't constitute a serious problem.

Commerce Department figures showed inventories swelled by $5.9 billion, or 1.3 percent, the largest rise in nine months, pushing the closely watched inventories-to-sales ratio to 1.51 from 1.44 in March -- the steepest monthly jump since 1967.

Separately, the Labor Department reported that initial claims for state unemployment insurance fell by 48,000 in the week ended May 31, possibly signaling a slowdown in the recent surge in the nation's unemployment rate.

At the same time, Ford National Bank of Boston, the nation's 17th largest commercial bank, lowered its prime lending rate to 12 percent, but it still wasn't clear late yesterday how quickly other banks would follow.

Meanwhile, the Labor Department published an industry-by-industry breakdown of productivity growth during 1979, showing sharp gains in the railroad and airline industries and visible declines in the service sector of the economy.

The 1.3 percent rise in inventory levels in April followed increases of 0.9 percent in March and 0.8 percent in February. Overall inventories stood at $445.2 billion, up from a revised $439.33 billion for March.

Inventories among manufacturing firms rose 1.7 percent over the month to $242.59 billion following a 1.5 percent boost in March, while stockbuilding by retailers expanded 1.1 percent to $110.33 billion after rising 3.5 percent in March.

Wholesalers' inventories leaped 6.5 percent in April after rising 0.2 percent in March. The April total for wholesalers was $92.3 billion compared with $91.71 billion in March.

The decline in initial claims for state unemployment insurance was welcome news for policymakers because the figure often presages changes in the overall unemployment rate. However, analysts said it is too early to draw any conclusions.

Initial claims for state unemployment insurance have surged sharply in recent weeks, reaching 673,000 before the latest drop. In the meantime, the nation's unemployment rate has soared to 7.8 percent, up from 6.2 percent two months ago.

The drop in the prime rate was in line with expectations. Most analysts have contended the prime is still too high in the face of current market conditions. The rate is the interest banks charge their most-creditworthy corporate customers.

Most banks still are maintaining a 13 percent prime, the rate that First National Bank of Boston held before announcing its reduction yesterday. The prime rose sharply earlier this year, reaching a record 20 percent before peaking in April.

The inventory figures have been watched closely by economists because excessive stockbuilding by businesses could lead to harsher production cutbacks. It was over-accumulation of inventories that worsened the 1974-75 recession.

Until the April report, inventory statistics had shown only moderate growth in business stockbuilding. Analysts said even with the April surge, however, inventories still were relatively lean and constituted no major threat.