Under the influence of a persistent stationary trough near California, the remains of the depression retraced westward back over the open waters of the Pacific. Advisories on the system were resumed late on September 20. Though it was reconsidered a tropical cyclone, its wind circulation was poorly defined; the depression again degenerated into an open trough at 0000 UTC September 22. Its forward motion remained relatively unchanged for several days, and by September 24 the system was reclassified as a tropical cyclone. After briefly drifting northward, the system began tracking toward the west-northwest. It gradually organized into a tropical storm at 0000 UTC September 25. Since it was then situated over favorable sea surface temperatures between and , Paul underwent a phase of rapid intensification. This allowed it to reach Category 1 hurricane strength on the Saffir-Simpson hurricane wind scale (SSHWS) just two days after its naming.