The conventional wisdom as per economic theory is that an increase in monetary supply leads to a decrease in interest rates. The circumstances that cause interest rates to rise are not natural ones—they result from the power of the Federal Open Market Committee, which itself includes members of the Federal Reserve Board (popularly known as "The Fed"). The Fed will raise interest rates to curb the inflation that would result if the monetary supply is exceeding large. It is important to note, however, that this is not a natural process.
Another consideration is what an increase in the monetary supply means. An increase in the money supply occurs when the Fed is buying securities from banks in the open market and the amount of reserves in the banking system rises. Because banks have more money to lend, the supply of money goes up. If demand remains the same, interest rates (the natural correcting force) should actually drop. The circumstance wherein interest rates increase is usually due artificial processes whereby the Fed raises rates itself to prevent rampant economic inflation.