If you wisely choose to remain silent at least until you have a chance to consult a lawyer, you should tell that to your interrogator. If you just keep your mouth shut and say nothing, the police can legally continue to question you and if they do you might eventually say something you later regret. (Somewhat ironically, the rule is that you have to say something to claim your right to remain silent.) However, you don't have to use any magic words to let police officers know that you want to remain silent. After an officer gives you a Miranda warning, you can stop the questioning by saying something like:
If the police continue to question you after you have asserted your right to remain silent, they have violated Miranda. As a result, anything you say after that point -- and any evidence gleaned from that conversation -- will not be admissible at your trial.