When I applied for a job, I indicated the desired working days from Tuesday to Sunday and set Monday as a day off. I thought that working on weekends should be paid extra. But my employer insists that

Short Answer: Yes, your employer is right; federal law does not require extra pay for weekend work unless it results in overtime.

Full Answer: The Fair Labor Standards Act (FLSA) does not require employers to pay extra for working on Saturdays or Sundays unless it leads to overtime (over 40 hours in a workweek), which must be paid at 1.5 times the regular rate.
Since the store operates seven days a week, your workdays of Tuesday to Sunday are considered part of the regular schedule, and weekend shifts do not qualify as days off unless specified by an employment contract or company policy.

The concept of weekends as days off is a common misconception; the legal definition of a day off depends on your agreed work schedule and the employer’s operating days. You would be entitled to only if your employment contract or company policy explicitly states extra pay for weekends.

Tip: Review your employee handbook or contract to clarify if there are any policies on weekend pay or shift differentials.

General Federal Standard: Extra pay for weekends is not federally mandated unless it exceeds 40 hours in a workweek, triggering overtime pay under the FLSA.