elicit
verb
the police claimed that his fingerprints had been found in order to elicit admissions from him:
obtain, bring out, draw out, extract, evoke, bring about, bring forth, induce, excite, give rise to, call forth, prompt, generate, engender, spark off, trigger, kindle;
extort, exact, wrest, derive, provoke, wring, screw, squeeze;
informal worm out.
elicit Oxford Dictionary of English