The Veterans' Memorial Preservation Act was enacted in 2003 and does not require Presidents' authorization despite his assertion.
However, such a law already exists in the United States. Congress passed a law in 2003 called the Veteran's Memorial Preservation and Recognition Act, which authorizes the government to impose a fine, a prison term of not more than ten years, or both on someone who destroys statues and monuments in the United States. President Trump also said that he plans to sign an executive order to bolster the 2003 law and reinforce it more uniformly. He did not elaborate on what that entails.