In California, the rules say that an employee who works more than 5 hours a day is entitled to a 30-minute meal break. If you work more than 10 hours in one stretch, you must also be given a second meal break.
If you work only 6 hours per day, you can waive your meal break. If you work 12 hours, you can waive your second meal break, if you’ve taken the first one.
Meal breaks are only applicable to non-exempt employees.
The quick answer is no. Your employer cannot require you to work while you are supposed to have a meal break. In effect, he is asking you to not eat and rather to work.
It is a whole different scenario if you voluntarily choose to work during your meal break.
It is a good practice. Managers should encourage employees to take their required breaks and counsel those who fail to do so.
Labor regulations say that your employer must give you a meal break. If he/she doesn’t, you may sue. In that case, you need a qualified and experienced attorney on your side.