diff --git a/src/Anon.cc b/src/Anon.cc
index 98d98a9f99..f8f580c1db 100644
--- a/src/Anon.cc
+++ b/src/Anon.cc
@@ -20,7 +20,7 @@ AnonymizeIPAddr* zeek::detail::ip_anonymizer[NUM_ADDR_ANONYMIZATION_METHODS] = {
 
 static uint32_t rand32()
 	{
-	return ((bro_random() & 0xffff) << 16) | (bro_random() & 0xffff);
+	return ((zeek::random_number() & 0xffff) << 16) | (zeek::random_number() & 0xffff);
 	}
 
 // From tcpdpriv.
diff --git a/src/Net.cc b/src/Net.cc
index 97940a792d..eaffe0b749 100644
--- a/src/Net.cc
+++ b/src/Net.cc
@@ -248,7 +248,7 @@ void net_packet_dispatch(double t, const Packet* pkt, iosource::PktSrc* src_ps)
 		if ( load_freq == 0 )
 			load_freq = uint32_t(0xffffffff) / uint32_t(load_sample_freq);
 
-		if ( uint32_t(bro_random() & 0xffffffff) < load_freq )
+		if ( uint32_t(zeek::random_number() & 0xffffffff) < load_freq )
 			{
 			// Drain the queued timer events so they're not
 			// charged against this sample.
diff --git a/src/PacketFilter.cc b/src/PacketFilter.cc
index 61afbe0afd..7b0ef0fbee 100644
--- a/src/PacketFilter.cc
+++ b/src/PacketFilter.cc
@@ -113,5 +113,5 @@ bool PacketFilter::MatchFilter(const Filter& f, const IP_Hdr& ip,
 			return false;
 		}
 
-	return uint32_t(bro_random()) < f.probability;
+	return uint32_t(zeek::random_number()) < f.probability;
 	}
diff --git a/src/util.cc b/src/util.cc
index ace3638e59..cccc65db8c 100644
--- a/src/util.cc
+++ b/src/util.cc
@@ -1211,7 +1211,7 @@ unsigned int bro_prng(unsigned int  state)
 	return zeek::prng(state);
 	}
 
-long int bro_random()
+long int zeek::random_number()
 	{
 	if ( ! bro_rand_determistic )
 		return random(); // Use system PRNG.
@@ -1221,6 +1221,11 @@ long int bro_random()
 	return bro_rand_state;
 	}
 
+long int bro_random()
+	{
+	return zeek::random_number();
+	}
+
 // Returns a 64-bit random string.
 uint64_t rand64bit()
 	{
@@ -1228,7 +1233,7 @@ uint64_t rand64bit()
 	int i;
 
 	for ( i = 1; i <= 4; ++i )
-		base = (base<<16) | bro_random();
+		base = (base<<16) | zeek::random_number();
 	return base;
 	}
 
@@ -2098,7 +2103,7 @@ uint64_t calculate_unique_id(size_t pool)
 			gettimeofday(&unique.time, 0);
 			unique.pool = (uint64_t) pool;
 			unique.pid = getpid();
-			unique.rnd = bro_random();
+			unique.rnd = static_cast<int>(zeek::random_number());
 
 			uid_instance = HashKey::HashBytes(&unique, sizeof(unique));
 			++uid_instance; // Now it's larger than zero.
diff --git a/src/util.h b/src/util.h
index b29a80d64b..e30b7650e5 100644
--- a/src/util.h
+++ b/src/util.h
@@ -202,7 +202,7 @@ extern std::string strstrip(std::string s);
 extern void hmac_md5(size_t size, const unsigned char* bytes,
 			unsigned char digest[16]);
 
-// Initializes RNGs for bro_random() and MD5 usage.  If load_file is given,
+// Initializes RNGs for zeek::random_number() and MD5 usage.  If load_file is given,
 // the seeds (both random & MD5) are loaded from that file.  This takes
 // precedence over the "use_empty_seeds" argument, which just
 // zero-initializes all seed values.  If write_file is given, the seeds are
@@ -225,6 +225,7 @@ unsigned int bro_prng(unsigned int state);
 
 // Replacement for the system random(), to which is normally falls back
 // except when a seed has been given. In that case, the function bro_prng.
+[[deprecated("Remove in v4.1.  Use zeek::random_number()")]]
 long int bro_random();
 
 // Calls the system srandom() function with the given seed if not running
@@ -599,4 +600,11 @@ void set_thread_name(const char* name, pthread_t tid = pthread_self());
  */
 long int prng(long int state);
 
+/**
+ * Wrapper for system random() in the default case, but when running in
+ * deterministic mode, uses the platform-independent zeek::prng()
+ * to obtain consistent results since implementations of rand() may vary.
+ */
+long int random_number();
+
 } // namespace zeek
diff --git a/src/zeek.bif b/src/zeek.bif
index f1af07ea36..253e2d8822 100644
--- a/src/zeek.bif
+++ b/src/zeek.bif
@@ -930,7 +930,7 @@ function hrw_weight%(key_digest: count, site_id: count%): count
 ##      provided by the OS.
 function rand%(max: count%): count
 	%{
-	auto result = bro_uint_t(double(max) * double(bro_random()) / (RAND_MAX + 1.0));
+	auto result = bro_uint_t(double(max) * double(zeek::random_number()) / (RAND_MAX + 1.0));
 	return zeek::val_mgr->Count(result);
 	%}
 
diff --git a/testing/btest/plugins/reader-plugin/src/Foo.cc b/testing/btest/plugins/reader-plugin/src/Foo.cc
index 4a05420bc3..6cae03ca18 100644
--- a/testing/btest/plugins/reader-plugin/src/Foo.cc
+++ b/testing/btest/plugins/reader-plugin/src/Foo.cc
@@ -45,10 +45,10 @@ std::string Foo::RandomString(const int len)
 	"abcdefghijklmnopqrstuvwxyz";
 
 	for (int i = 0; i < len; ++i)
-		// bro_random is not thread-safe; as we are only using one simultaneous thread
+		// zeek::random_number() is not thread-safe; as we are only using one simultaneous thread
 		// here, this should not matter in this case. If this test ever starts showing
 		// random errors, this might be the culprit.
-		s[i] = values[bro_random() / (RAND_MAX / sizeof(values))];
+		s[i] = values[zeek::random_number() / (RAND_MAX / sizeof(values))];
 
 	return s;
 	}