diff --git a/include/bout/solver.hxx b/include/bout/solver.hxx
index 3413fb2a82..d8d3318151 100644
--- a/include/bout/solver.hxx
+++ b/include/bout/solver.hxx
@@ -416,8 +416,8 @@ protected:
   std::string run_id = "zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz";
   /// The run from which this was restarted.
   std::string run_restart_from = "yyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy";
-  /// Generate a random UUID and broadcast it to all processors
-  std::string createRunId();
+  /// Generate a random UUID (version 4) and broadcast it to all processors
+  std::string createRunId() const;
 
   /// Run the user's RHS function
   int run_rhs(BoutReal t);
diff --git a/src/solver/solver.cxx b/src/solver/solver.cxx
index 3e55d84d3a..1c51016db7 100644
--- a/src/solver/solver.cxx
+++ b/src/solver/solver.cxx
@@ -529,20 +529,26 @@ int Solver::solve(int NOUT, BoutReal TIMESTEP) {
   return status;
 }
 
-std::string Solver::createRunId() {
+std::string Solver::createRunId() const {
 
   std::string result;
   result.resize(36);
 
   if (MYPE == 0) {
-    std::random_device rd;
-    auto seed_data = std::array<int, std::mt19937::state_size> {};
-    std::generate(std::begin(seed_data), std::end(seed_data), std::ref(rd));
-    std::seed_seq seq(std::begin(seed_data), std::end(seed_data));
-    std::mt19937 generator(seq);
-    uuids::uuid_random_generator gen{generator};
-
-    result = uuids::to_string(gen()); // Different each time the simulation is run
+    // Generate a unique ID for this run
+    if (bout::build::has_uuid_system_generator) {
+      uuids::uuid_system_generator gen{};
+      result = uuids::to_string(gen());
+    } else {
+      std::random_device rd;
+      auto seed_data = std::array<int, std::mt19937::state_size> {};
+      std::generate(std::begin(seed_data), std::end(seed_data), std::ref(rd));
+      std::seed_seq seq(std::begin(seed_data), std::end(seed_data));
+      std::mt19937 generator(seq);
+      uuids::uuid_random_generator gen{generator};
+
+      result = uuids::to_string(gen());
+    }
   }
 
   // All ranks have same run_id