My table has two DATE format attributes, however, when i try to insert value it throws an error: date format picture ends before converting entire input string.
What you're trying to insert is not a date, I think, but a string. You need to use to_date() function, like this:
to_date()
insert into table t1 (id, date_field) values (1, to_date('20.06.2013', 'dd.mm.yyyy'));