If you can control the NLS territory setting (or even better: you want to adapt to it), then the simplest solution is to use TRUNC(SYSDATE,'D') and TRUNC(SYSDATE,'D')+6 :
alter session set nls_territory='saudi arabia';
select today
, trunc(today,'D') start_date
, trunc(today,'D') + 6 end_date
from (select date '2018-02-28'+level today from dual connect by level<=10);
The above query adapts to the week definition for a given territory: the week will start on Sunday in US and on Monday in Europe. It will start on Saturday in Arabic countries.
If you want to hardcode the week start to Saturday and make it independent of NLS settings, then you need to do some more complex date arithmetic, because TRUNC does not accept NLS_TERRITORY as a direct parameter:
select today
, today - mod(to_number(to_char(today,'J')) - 2415026,7) start_date
, today - mod(to_number(to_char(today,'J')) - 2415026,7) + 6 end_date
from (select date '2018-02-28'+level today from dual connect by level<=10);
The above query uses the Julian date (2415026) of the first Saturday in the 20th century (January 6th, 1900) as an anchor point. (You could use any Saturday before your oldest "today" as the anchor.) The modulo (MOD) expression returns 0 if today is Saturday, 1 if it is Sunday, etc. This offset is subtracted from today, giving the closest Saturday before today. The end date is obviously the start date plus 6 days. By moving the anchor date slightly, you can hardcode any day as the first day of a week.
Correction to your example: if today is 02/mar/2018 then start date is 24/feb/2018 but end date is 02/mar/2018, not 03/mar/2018.