Can Capital Loss from the sell of securities claimed on individual Tax return be used to offset the taxes due on an interest received from personal Bank savings accounts such as money market or CD.?

Can Capital Loss from the sell of securities claimed on individual Tax return be used to offset the taxes due on an interest received from personal Bank savings accounts such as money market or CD.?
No, not directly. As you noted, securities investments are reported as capital gains or losses, and taxed (at a lower rate). Interest is taxed as ordinary income.