When someone says "don't worry", they are trying to reassure you and alleviate any concerns you may have. There are many synonyms for this phrase that can be used in various contexts. "Don't fret" is a common alternative that is often used in a casual conversation. "Don't stress" is another popular phrase that implies that there is no need to get anxious or worked up. Other synonyms include "relax", "take it easy", "calm down". No matter which phrase you use, the sentiment is the same - there is no need to worry or be anxious about something.
