The rocker, posted an emotional video message on his Facebook page addressing the controversy over the phrase, which campaigners claim aims to belittle the Black Lives Matter movement.
Black Lives Matter was founded by U.S. activists after the 2012 murder of African-American teen Trayvon Martin to demand justice and highlight the deaths of young black men in police custody.
The controversy over the phrase "all lives matter" has become especially pronounced after two African-American men died at the hands of police, and five police officers were shot dead by a gunman during a Dallas, Texas Black Lives Matter protest against the deaths.
Several musicians have been criticised after declaring "all lives matter", including Jennifer Lopez and The Cult musician Ian Astbury.
However, Corey said in his message, "It has been kind of crazy lately, and some of the voices that are out there are saying one thing, trying to pull us apart, splitting hairs and taking various unifying messages and ripping them to shreds beneath the minutiae of just pretentious ignorance.To me, it's very simple. We all matter...
"You can back up 'black lives matter' and say that cops' lives matter; it's all the same thing. And you can have those different ideas in the same thought, and there's nothing wrong with that, because we do all matter."
The Wait and Bleed musician also said that he sees a role for music in healing America's racial tension and social problems.
He added, "The thing that I've realised is that if music can bring us all together and get us all to care about one another and tear down those colour lines, those personality lines, those lines that try to keep us different, if music can rip all of that down, then we can all band together and say, 'Well, if music can bring us together, maybe life in itself is the best way to bring us all together and keep us there.'"
The shootings and resulting anger have caused U.S. President Barack Obama to issue a plea for unity amid fears that America will return to the dark days of the 1960s when simmering racial tensions resulted in mass riots.