Went to a local ICICI bank to purchase a Fastag. The branch executive had no clue (or played dumb intentionally) and told that fastag can be purchased only after opening an icici savings account.

I already have a SBI account, but I cannot purchase Fastag from SBI website directly. Apparently, this is not available to encourage private players (like PayTM who sell online), as per ex-employees ;-)

OMR has a toll booth but they don't sell FASTags there.