In Oedipus Rex, did the oracle at Delphi tell Oedipus to stay at Corinth?

In Oedipus Rex, the oracle at Delphi does not tell Oedipus to leave Corinth.  Oedipus hears a rumor that his parents are not his true parents, so he goes to consult the oracle to find out if the rumor is true.  But the oracle does not directly answer Oedipus' question; instead, the oracle tells Oedipus that he is destined to kill his father and bear children with his mother.  Horrified by this prophecy, Oedipus decides that the best thing to do is to leave Corinth in an effort to protect Polybus and Merope.  Once he makes the decision to leave, Oedipus does not try any more to get information on his original question, and he does not find out about his true parentage until much later when the old shepherd is brought before him to relay the acts of the past.  Thus, the oracle does not tell Oedipus to leave Corinth, nor does it tell him to stay--the oracle has an unexpected message for Oedipus.