That is not entirely accurate.
What you are talking about is physical currency, and it would be correct to say that the creation of physical money is a function between the Fed and the US Department of the Treasury.
However, well north of 90% of our money system is digital. How that is controlled, rather influenced, is very different.
What
@JohnfrmClevelan is talking about is spot on. Every single time a bank makes a loan to a business or person it simultaneously creates a balance sheet 'deposit' in the borrowers bank account, in that act literally money is created by the bank notating the difference between an asset and a liability with an emphasis on reserves by regulated percentages. Something very similar occurs when the business or a person pays off the loan in reverse, most of those dollars are extinguished (against that balance sheet entry.)
This is influenced, greatly, by interest rate controls which is Fed monetary policy. And can be influenced further by Fed actions like buying and selling assets.
Go to the Fed yourself, and you will see how much this occurs and see that on average just the act of making loans increases the amount of digital currency well above 10% per year on average.
All of this is possible because there are multiple banks in our financial system all of whom only have to hold a fraction of their deposits as reserves, the rest is loaned out even between banks. Deposits increase and by effect so does the money supply.