Industrial production rose by a modest 0.3 percent last month, while housing starts plummeted by 14 percent to 1.152 million units, the lowest level since last year's recession, according to official reports released yesterday.

Against this background of an apparently slowing economy Citibank, the nation's second largest, and Bankers Trust Co. lowered their prime lending rate 1/2 point to 19 1/2 percent. This followed Chemical Bank's 1 percentage point cut in the prime last Friday.

The slight rise in the nation's industrial output, reported by the Federal Reserve for last month, followed a downwardly revised 0.1 percent increase in production in April. Much of last month's improvement was "concentrated in production of mother vehicles and parts," the Fed said.

The production of the new J car by General Motors helped to boost the month's figures, as did a general buildup of inventories by auto dealers. Analysts said that the production rise therefore did not indicate strength in the economy.

David Cross, economist at Chase Econometrics private forecasters, said the 7 1/2 percent increase in auto assemblies, to an annual rate of 7.3 million units, "certainly had nothing to do with sales." Dealers have to build up inventories in the spring "in anticipation of plant closings over the summer," he said.

A Commerce Department spokesman said the April and May production figures "are consistent with the theme that we're going to have -- and that we're having -- a very sluggish economy." The administration is predicting a flat economy for the middle of the year.

The slowdown is helping to bring down interest rates that soared during the spring. Treasury Undersecretary for Monetary Affairs Beryl Sprinkel said yesterday that the economics pain caused by high interest rates "has peaked and is receding."

Despite the sharp fall in housing starts last month, they remained 23 percent above their level of a year earlier. "While the immediate future of the housing industry is not rosy, we are seeing some initial decline in inflation and more recently in interest rates," said Commerce Secretary Malcolm Baldrige.

Within the total industrial production figures, manufacturing output was up by 0.4 percent (equal to the April rise); mining output was down 0.4 percent, because of the strike, and utilities output was up by 0.3 percent. 0