Widebody Transport
Flight Crew Air Transport Pilot (ATP)
Communication Breakdown; Time Pressure
ATC Issue All Types; Deviation - Track / Heading All Types; Inflight Event / Encounter Weather / Turbulence
Flight Crew Returned To Clearance
Weather
About 3+26 into flight at FL330; after passing N46E170; we encountered moderate to severe turbulence with associated 'pop-up' radar returns beneath the aircraft. We couldn't see as we were at the cloud tops. As Pilot Monitoring; I sent SF Radio [ARINC] a message requesting left deviation for weather; we had radar indications that prevented a right deviation. SF Radio's response wasn't timely enough and we decided to deviate left off of our Strategic Lateral Offset Procedure. We reviewed the Long Range Navigation (LRN) for weather deviations and were aware of parameters and altitude requirements of a deviation off course for weather. Our left deviation kept the aircraft at a safe distance away magenta indications on the radar. SF Radio replied with 'unable deviation left due to traffic.' By this time we had already deviated left. Upon receiving this message the flying pilot turned right to return on course; while avoiding weather. SF Radio sent another message indicating they showed us off course. We replied that we were back on course.Intent is to communicate why we deviated for weather and that the crew was aware of off track deviation procedures.
[Report narrative contained no additional information.]
Air Carrier flight crew reported a deviation for weather in oceanic airspace; after deviating a message was received from ATC that denied the deviation.