The first move can win the game. It's a matter of consequence. Waiting until after the mob is at your door to issue a statement makes you look at best uninformed, and at worst guilty of attempted cover-up - or on the killers' side.

Even if this doesn't escalate, issuing a statement will give the appearance of being in control and proactive. Who could fault you for that?

You have an advantage; don't lose it to time.