Another alternative if you don't need a lot of holding strength is to pre-drill the hole, partly fill with epoxy, then screw as securely as possible (tight, but shy of stripping out). Wipe up any epoxy that escapes.Then allow the epoxy to set and harden. It also helps to use as long a screw as practical for such applications (not just the short screws that came with the hardware). Just beware that if you apply too much epoxy, and then drive the screw in, you may find epoxy leaking out of interesting places since it will migrate (under pressure) to wherever there are flaws in the wood (or plywood), so squirt a little epoxy in the hole and then coat the screw threads.
However, Mike's suggestion is by far the most preferred solution, especially where maximum strength is required.