diff --git a/src/csharp/Grpc.Core/IAsyncStreamReader.cs b/src/csharp/Grpc.Core/IAsyncStreamReader.cs
index 42bfbb87e01..4a169fcca5d 100644
--- a/src/csharp/Grpc.Core/IAsyncStreamReader.cs
+++ b/src/csharp/Grpc.Core/IAsyncStreamReader.cs
@@ -41,6 +41,11 @@ namespace Grpc.Core
     /// (<c>MoveNext</c> will return <c>false</c>) and the <c>CancellationToken</c>
     /// associated with the call will be cancelled to signal the failure.
     /// </para>
+    /// <para>
+    /// <c>MoveNext()</c> operations can be cancelled via a cancellation token. Cancelling
+    /// an individual read operation has the same effect as cancelling the entire call
+    /// (which will also result in the read operation returning prematurely).
+    /// </para>
     /// </summary>
     /// <typeparam name="T">The message type.</typeparam>
     public interface IAsyncStreamReader<T> : IAsyncEnumerator<T>
diff --git a/src/csharp/Grpc.Core/Internal/ClientResponseStream.cs b/src/csharp/Grpc.Core/Internal/ClientResponseStream.cs
index 851b6ca213c..ab649ee7662 100644
--- a/src/csharp/Grpc.Core/Internal/ClientResponseStream.cs
+++ b/src/csharp/Grpc.Core/Internal/ClientResponseStream.cs
@@ -49,19 +49,19 @@ namespace Grpc.Core.Internal
 
         public async Task<bool> MoveNext(CancellationToken token)
         {
-            if (token != CancellationToken.None)
+            var cancellationTokenRegistration = token.CanBeCanceled ? token.Register(() => call.Cancel()) : (IDisposable) null;
+            using (cancellationTokenRegistration)
             {
-                throw new InvalidOperationException("Cancellation of individual reads is not supported.");
-            }
-            var result = await call.ReadMessageAsync().ConfigureAwait(false);
-            this.current = result;
+                var result = await call.ReadMessageAsync().ConfigureAwait(false);
+                this.current = result;
 
-            if (result == null)
-            {
-                await call.StreamingResponseCallFinishedTask.ConfigureAwait(false);
-                return false;
+                if (result == null)
+                {
+                    await call.StreamingResponseCallFinishedTask.ConfigureAwait(false);
+                    return false;
+                }
+                return true;
             }
-            return true;
         }
 
         public void Dispose()
diff --git a/src/csharp/Grpc.Core/Internal/ServerRequestStream.cs b/src/csharp/Grpc.Core/Internal/ServerRequestStream.cs
index c65b960afb2..058dddb7ebb 100644
--- a/src/csharp/Grpc.Core/Internal/ServerRequestStream.cs
+++ b/src/csharp/Grpc.Core/Internal/ServerRequestStream.cs
@@ -49,13 +49,14 @@ namespace Grpc.Core.Internal
 
         public async Task<bool> MoveNext(CancellationToken token)
         {
-            if (token != CancellationToken.None)
+            
+            var cancellationTokenRegistration = token.CanBeCanceled ? token.Register(() => call.Cancel()) : (IDisposable) null;
+            using (cancellationTokenRegistration)
             {
-                throw new InvalidOperationException("Cancellation of individual reads is not supported.");
+                var result = await call.ReadMessageAsync().ConfigureAwait(false);
+                this.current = result;
+                return result != null;
             }
-            var result = await call.ReadMessageAsync().ConfigureAwait(false);
-            this.current = result;
-            return result != null;
         }
 
         public void Dispose()