diff --git a/pkg/util/errors.go b/pkg/util/errors.go
index 87efe4185d..70b1475f74 100644
--- a/pkg/util/errors.go
+++ b/pkg/util/errors.go
@@ -78,6 +78,41 @@ func (es MultiError) Is(target error) bool {
 	return true
 }
 
+// IsCancel tells if all errors are either context.Canceled or grpc codes.Canceled.
+func (es MultiError) IsCancel() bool {
+	if len(es) == 0 {
+		return false
+	}
+	for _, err := range es {
+		if errors.Is(err, context.Canceled) {
+			continue
+		}
+		if IsConnCanceled(err) {
+			continue
+		}
+		return false
+	}
+	return true
+}
+
+// IsDeadlineExceeded tells if all errors are either context.DeadlineExceeded or grpc codes.DeadlineExceeded.
+func (es MultiError) IsDeadlineExceeded() bool {
+	if len(es) == 0 {
+		return false
+	}
+	for _, err := range es {
+		if errors.Is(err, context.DeadlineExceeded) {
+			continue
+		}
+		s, ok := status.FromError(err)
+		if ok && s.Code() == codes.DeadlineExceeded {
+			continue
+		}
+		return false
+	}
+	return true
+}
+
 // IsConnCanceled returns true, if error is from a closed gRPC connection.
 // copied from https://github.com/etcd-io/etcd/blob/7f47de84146bdc9225d2080ec8678ca8189a2d2b/clientv3/client.go#L646
 func IsConnCanceled(err error) bool {
diff --git a/pkg/util/server/error.go b/pkg/util/server/error.go
index da41c229ad..05ee1bc510 100644
--- a/pkg/util/server/error.go
+++ b/pkg/util/server/error.go
@@ -5,6 +5,11 @@ import (
 	"errors"
 	"net/http"
 
+	"google.golang.org/grpc/codes"
+	"google.golang.org/grpc/status"
+
+	"github.com/grafana/loki/pkg/util"
+
 	"github.com/prometheus/prometheus/promql"
 	"github.com/weaveworks/common/httpgrpc"
 	"github.com/weaveworks/common/user"
@@ -28,11 +33,24 @@ func WriteError(err error, w http.ResponseWriter) {
 		promErr  promql.ErrStorage
 	)
 
+	me, ok := err.(util.MultiError)
+	if ok && me.IsCancel() {
+		http.Error(w, ErrClientCanceled, StatusClientClosedRequest)
+		return
+	}
+	if ok && me.IsDeadlineExceeded() {
+		http.Error(w, ErrDeadlineExceeded, http.StatusGatewayTimeout)
+		return
+	}
+
+	s, isRPC := status.FromError(err)
 	switch {
 	case errors.Is(err, context.Canceled) ||
+		(isRPC && s.Code() == codes.Canceled) ||
 		(errors.As(err, &promErr) && errors.Is(promErr.Err, context.Canceled)):
 		http.Error(w, ErrClientCanceled, StatusClientClosedRequest)
-	case errors.Is(err, context.DeadlineExceeded):
+	case errors.Is(err, context.DeadlineExceeded) ||
+		(isRPC && s.Code() == codes.DeadlineExceeded):
 		http.Error(w, ErrDeadlineExceeded, http.StatusGatewayTimeout)
 	case errors.As(err, &queryErr):
 		http.Error(w, err.Error(), http.StatusBadRequest)
diff --git a/pkg/util/server/error_test.go b/pkg/util/server/error_test.go
index 948ed2fb9a..07975ab84a 100644
--- a/pkg/util/server/error_test.go
+++ b/pkg/util/server/error_test.go
@@ -9,6 +9,9 @@ import (
 	"net/http/httptest"
 	"testing"
 
+	"google.golang.org/grpc/codes"
+	"google.golang.org/grpc/status"
+
 	"github.com/prometheus/prometheus/promql"
 	"github.com/stretchr/testify/require"
 	"github.com/weaveworks/common/httpgrpc"
@@ -29,9 +32,18 @@ func Test_writeError(t *testing.T) {
 	}{
 		{"cancelled", context.Canceled, ErrClientCanceled, StatusClientClosedRequest},
 		{"cancelled multi", util.MultiError{context.Canceled, context.Canceled}, ErrClientCanceled, StatusClientClosedRequest},
+		{"rpc cancelled", status.New(codes.Canceled, context.Canceled.Error()).Err(), ErrClientCanceled, StatusClientClosedRequest},
+		{"rpc cancelled multi", util.MultiError{status.New(codes.Canceled, context.Canceled.Error()).Err(), status.New(codes.Canceled, context.Canceled.Error()).Err()}, ErrClientCanceled, StatusClientClosedRequest},
+		{"mixed context and rpc cancelled", util.MultiError{context.Canceled, status.New(codes.Canceled, context.Canceled.Error()).Err()}, ErrClientCanceled, StatusClientClosedRequest},
+		{"mixed context, rpc cancelled and another", util.MultiError{errors.New("standard error"), context.Canceled, status.New(codes.Canceled, context.Canceled.Error()).Err()}, "3 errors: standard error; context canceled; rpc error: code = Canceled desc = context canceled", http.StatusInternalServerError},
 		{"cancelled storage", promql.ErrStorage{Err: context.Canceled}, ErrClientCanceled, StatusClientClosedRequest},
 		{"orgid", user.ErrNoOrgID, user.ErrNoOrgID.Error(), http.StatusBadRequest},
 		{"deadline", context.DeadlineExceeded, ErrDeadlineExceeded, http.StatusGatewayTimeout},
+		{"deadline multi", util.MultiError{context.DeadlineExceeded, context.DeadlineExceeded}, ErrDeadlineExceeded, http.StatusGatewayTimeout},
+		{"rpc deadline", status.New(codes.DeadlineExceeded, context.DeadlineExceeded.Error()).Err(), ErrDeadlineExceeded, http.StatusGatewayTimeout},
+		{"rpc deadline multi", util.MultiError{status.New(codes.DeadlineExceeded, context.DeadlineExceeded.Error()).Err(), status.New(codes.DeadlineExceeded, context.DeadlineExceeded.Error()).Err()}, ErrDeadlineExceeded, http.StatusGatewayTimeout},
+		{"mixed context and rpc deadline", util.MultiError{context.DeadlineExceeded, status.New(codes.DeadlineExceeded, context.DeadlineExceeded.Error()).Err()}, ErrDeadlineExceeded, http.StatusGatewayTimeout},
+		{"mixed context, rpc deadline and another", util.MultiError{errors.New("standard error"), context.DeadlineExceeded, status.New(codes.DeadlineExceeded, context.DeadlineExceeded.Error()).Err()}, "3 errors: standard error; context deadline exceeded; rpc error: code = DeadlineExceeded desc = context deadline exceeded", http.StatusInternalServerError},
 		{"parse error", logqlmodel.ParseError{}, "parse error : ", http.StatusBadRequest},
 		{"httpgrpc", httpgrpc.Errorf(http.StatusBadRequest, errors.New("foo").Error()), "foo", http.StatusBadRequest},
 		{"internal", errors.New("foo"), "foo", http.StatusInternalServerError},