Learjet 60
Flight Crew Flight Instructor; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Flight Crew Last 90 Days 93; Flight Crew Total 7700; Flight Crew Type 2200
Time Pressure; Situational Awareness; Other / Unknown; Distraction; Workload
Aircraft Equipment Problem Less Severe; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Provided Assistance; Air Traffic Control Issued Advisory / Alert; Flight Crew Became Reoriented
Aircraft
Upon departure from XYR at ZZZ; I received a false terrain alert from the TAWS system.  That caused to delay the activation of the 'nav' mode on my flight director which delayed my turn to the ZZZZZ intersection.  ATC gave me an expedited turn to a heading of 350 to get me headed toward ZZZZZ.  Based on what I saw on my TCAS; I don't believe there was a loss of separation.
Lear 60 Captain reported deviating off course after departure due to receiving a false TAWS warning for terrain. ATC gave the pilot a new heading and the flight continued on the correct routing.