Short-term interest rates, which plummeted Monday following some political sparring between President Carter and Federal Reserve Board Chairman Paul A. Volcker, rose slightly today after the Federal Reserve took steps to keep its monetary policy tight.

Long-term government bond prices fell sharply in late trading after the Treasury announced that it had auctioned $1.5 billion of 15-year bonds at an average yield of 11.61 percent.

Bond prices had dropped during the afternoon, according to William Sullivan, vice president of the Bank of New York, as market participants realized there was little "retail" interest in the new 15-year Treasury security.

Just before the results were announced, the new bonds were trading at a yield of between 11.6 and 11.63 percent (on what dealers call a "when-issued" basis). As soon as the Treasury announced the results -- which contained a wide range of bids -- the yield on the bonds immediately jumped to about 11.7 percent.

When bond yields go up, bond prices fall.

The bonds, when issued by the Treasury, will carry a coupon that pays 11 1/2 percent on the face value of the bond. The Treasury already was selling them at a price lower than their face value to reach an 11.61 yield (actually that was the average; some bidders will get a yield as high as 11.75 percent).

The bonds auctioned today already have dropped from their face value of $1,000 to $986.30. Before the Treasury announced the results of the auction late this afternoon, bonds had been trading at about $992.00.

Sullivan said that most other long-term government securities also declined in price today -- ranging from $5 to $7.50 on a face value of $1,000.

Because of the Fed's new tightening move -- it drained bank reserves when the key federal funds rate was down to about 11 3/4 percent -- and the increase in long-term interest rates, as well, analysts said that today's announcement by Citibank and Marine Midland Bank (that they were reducing their broker loan rates to 13 percent from 14 percent) should not be taken as a signal that interest rates are about to fall. Often the fall in the rate charged stock brokers precedes a cut in the prime lending rate -- the interest banks charge their top corporate customers for a short-term loan.

Most banks have a prime rate of 13 1/2 percent, although a handful, including Citibank, charge 14 percent.

With its intervention when federal funds were trading at 11 3/4 percent, the central bank "apparently is going to support a federal funds rate of 12 percent," according to Bank of New York's Sullivan. Federal funds are excess reserves that banks trade among themselves overnight and the interest on federal funds is one the central bank can control.

Sullivan said that the resistance to the new Treasury issue on the part of most investors is due to everyone's "lack of appetite for investing in a 15-year security."