diff --git a/src/test/fuzz/p2p_headers_presync.cpp b/src/test/fuzz/p2p_headers_presync.cpp
index 3a7146df8fe..b31b74ee4fe 100644
--- a/src/test/fuzz/p2p_headers_presync.cpp
+++ b/src/test/fuzz/p2p_headers_presync.cpp
@@ -32,6 +32,12 @@ public:
         PeerManager::Options peerman_opts;
         node::ApplyArgsManOptions(*m_node.args, peerman_opts);
         peerman_opts.max_headers_result = FUZZ_MAX_HEADERS_RESULTS;
+        // The peerman's rng is a global that is re-used, so it will be re-used
+        // and may cause non-determinism between runs. This may even influence
+        // the global RNG, because seeding may be done from the gloabl one. For
+        // now, avoid it influencing the global RNG, and initialize it with a
+        // constant instead.
+        peerman_opts.deterministic_rng = true;
         // No txs are relayed. Disable irrelevant and possibly
         // non-deterministic code paths.
         peerman_opts.ignore_incoming_txs = true;