diff --git a/akka-projection-grpc/src/main/scala/akka/projection/grpc/internal/FilterStage.scala b/akka-projection-grpc/src/main/scala/akka/projection/grpc/internal/FilterStage.scala
index 8814c2120..b1db1b8ef 100644
--- a/akka-projection-grpc/src/main/scala/akka/projection/grpc/internal/FilterStage.scala
+++ b/akka-projection-grpc/src/main/scala/akka/projection/grpc/internal/FilterStage.scala
@@ -4,11 +4,12 @@
 
 package akka.projection.grpc.internal
 
+import akka.Done
+
 import scala.util.Failure
 import scala.util.Success
 import scala.util.Try
 import scala.util.matching.Regex
-
 import akka.NotUsed
 import akka.actor.typed.scaladsl.LoggerOps
 import akka.annotation.InternalApi
@@ -28,6 +29,7 @@ import akka.stream.Attributes
 import akka.stream.BidiShape
 import akka.stream.Inlet
 import akka.stream.Outlet
+import akka.stream.scaladsl.Keep
 import akka.stream.scaladsl.Sink
 import akka.stream.scaladsl.SinkQueueWithCancel
 import akka.stream.scaladsl.Source
@@ -37,6 +39,8 @@ import akka.stream.stage.InHandler
 import akka.stream.stage.OutHandler
 import org.slf4j.LoggerFactory
 
+import scala.concurrent.Future
+
 /**
  * INTERNAL API
  */
@@ -145,7 +149,8 @@ import org.slf4j.LoggerFactory
   private case class ReplaySession(
       fromSeqNr: Long,
       filterAfterSeqNr: Long,
-      queue: SinkQueueWithCancel[EventEnvelope[Any]])
+      queue: SinkQueueWithCancel[EventEnvelope[Any]],
+      replayStreamCompletion: Future[Done])
 
 }
 
@@ -356,11 +361,14 @@ import org.slf4j.LoggerFactory
               replayInProgress(pid).copy(filterAfterSeqNr = replayPersistenceId.filterAfterSeqNr))
           } else if (replayInProgress.size < replayParallelism) {
             log.debugN("Stream [{}]: Starting replay of persistenceId [{}], from seqNr [{}]", logPrefix, pid, fromSeqNr)
-            val queue =
+            val (replayCompletion, queue) =
               currentEventsByPersistenceId(pid, fromSeqNr)
-                .runWith(Sink.queue())(materializer)
-            replayInProgress =
-              replayInProgress.updated(pid, ReplaySession(fromSeqNr, replayPersistenceId.filterAfterSeqNr, queue))
+                .watchTermination()((_, done) => done)
+                .toMat(Sink.queue())(Keep.both)
+                .run()(materializer)
+            replayInProgress = replayInProgress.updated(
+              pid,
+              ReplaySession(fromSeqNr, replayPersistenceId.filterAfterSeqNr, queue, replayCompletion))
             tryPullReplay(pid)
           } else {
             log.debugN("Stream [{}]: Queueing replay of persistenceId [{}], from seqNr [{}]", logPrefix, pid, fromSeqNr)
@@ -457,12 +465,36 @@ import org.slf4j.LoggerFactory
         }
       })
 
-      setHandler(outEnv, new OutHandler {
-        override def onPull(): Unit = {
-          log.trace("Stream [{}]: onPull outEnv", logPrefix)
-          pullInEnvOrReplay()
-        }
-      })
+      setHandler(
+        outEnv,
+        new OutHandler {
+          override def onPull(): Unit = {
+            log.trace("Stream [{}]: onPull outEnv", logPrefix)
+            pullInEnvOrReplay()
+          }
+
+          override def onDownstreamFinish(cause: Throwable): Unit = {
+            val runningSessions = replayInProgress.values.filterNot(_.replayStreamCompletion.isCompleted)
+            if (runningSessions.nonEmpty) {
+              // to avoid abrupt stage termination error logging,
+              // defer acting on cancel until any replays have completely cancelled
+              setKeepGoing(true)
+              val replayCompletedCallback = getAsyncCallback[Try[Done]] { _ =>
+                val stillRunning = replayInProgress.values.filterNot(_.replayStreamCompletion.isCompleted)
+                if (stillRunning.isEmpty) {
+                  super.onDownstreamFinish(cause)
+                }
+              }.invoke _
+              runningSessions.foreach { runningSession =>
+                runningSession.queue.cancel()
+                runningSession.replayStreamCompletion.onComplete(replayCompletedCallback)(ExecutionContexts.parasitic)
+              }
+            } else {
+              super.onDownstreamFinish(cause)
+            }
+          }
+        })
+
     }
 
 }