The answer to this question is complicated because the way the Fed operates has changed over time. In particular, Quantitative Easing (QE) changed things a lot.
Firstly, the Fed largely controls the Fed Funds rate, which is an overnight inter-bank rate. Other interest rates are set as a spread to that rate, but are not directly controlled by the Fed. Instead, those rates are generally set by what market participants expect the Fed to do.
Secondly, we need to be careful about what “money supply” you are talking about. The Fed directly operates on the monetary base, since that roughly corresponds to the size of its balance sheet. Other monetary aggregates include other instruments that the Fed cannot directly control.
In the pre-QE era, the Fed could control interest rates by creating/destroying bank reserves - a major component of the monetary base. Banks lend reserves to eachother in the Fed Funds market. If there is a shortage of reserves, banks will bid up the cost of reserves - the Fed Funds rate. The Fed creates reserves by buying bonds (or lending against them),and withdraws reserves by selling them. They need to conduct operations to keep interest rates near target.
However, the Fed is effectively forced to supply whatever reserves are needed by the banking system, otherwise they will fail their reserves requirements. Central bankers started listening to Monetarists in the 1970s, and tried setting their interest rate target so that money growth would hit a target rate. However, since they did not publicly acknowledge that they had a target interest rate, it appeared that they were targeting the money supply.
In the post-QE era, there is an excess of reserves in the system, so there is no issue of banks being short. Interest rates are instead determined by the level of interest paid on reserves, which can evolve completely independently of monetary aggregates.