diff --git a/app/victoria-logs/Makefile b/app/victoria-logs/Makefile
index 6b2170613..7c8054418 100644
--- a/app/victoria-logs/Makefile
+++ b/app/victoria-logs/Makefile
@@ -101,3 +101,10 @@ victoria-logs-windows-amd64:
 
 victoria-logs-pure:
 	APP_NAME=victoria-logs $(MAKE) app-local-pure
+
+run-victoria-logs:
+	mkdir -p victoria-logs-data
+	DOCKER_OPTS='-v $(shell pwd)/victoria-logs-data:/victoria-logs-data' \
+	APP_NAME=victoria-logs \
+	ARGS='' \
+	$(MAKE) run-via-docker
diff --git a/docs/VictoriaLogs/CHANGELOG.md b/docs/VictoriaLogs/CHANGELOG.md
index 2fcab1a4d..fb7c3d6a9 100644
--- a/docs/VictoriaLogs/CHANGELOG.md
+++ b/docs/VictoriaLogs/CHANGELOG.md
@@ -34,6 +34,7 @@ according to [these docs](https://docs.victoriametrics.com/VictoriaLogs/QuickSta
 
 * BUGFIX: fix `invalid memory address or nil pointer dereference` panic when using [`extract`](https://docs.victoriametrics.com/victorialogs/logsql/#extract-pipe), [`unpack_json`](https://docs.victoriametrics.com/victorialogs/logsql/#unpack_json-pipe) or [`unpack_logfmt`](https://docs.victoriametrics.com/victorialogs/logsql/#unpack_logfmt-pipe) pipes. See [this issue](https://github.com/VictoriaMetrics/VictoriaMetrics/issues/6306).
 * BUGFIX: [web UI](https://docs.victoriametrics.com/VictoriaLogs/querying/#web-ui): fix an issue where logs with long `_msg` values might not display. See [this issue](https://github.com/VictoriaMetrics/VictoriaMetrics/issues/6281).
+* BUGFIX: properly handle time range boundaries with millisecond precision. See [this issue](https://github.com/VictoriaMetrics/VictoriaMetrics/issues/6293).
 
 ## [v0.8.0](https://github.com/VictoriaMetrics/VictoriaMetrics/releases/tag/v0.8.0-victorialogs)
 
diff --git a/lib/logstorage/parser.go b/lib/logstorage/parser.go
index 536b0016e..49b677b68 100644
--- a/lib/logstorage/parser.go
+++ b/lib/logstorage/parser.go
@@ -1307,7 +1307,8 @@ func parseFilterTime(lex *lexer) (*filterTime, error) {
 			if err != nil {
 				return nil, fmt.Errorf("cannot parse _time filter: %w", err)
 			}
-			startTime := int64(t * 1e9)
+			// Round to milliseconds
+			startTime := int64(math.Round(t*1e3)) * 1e6
 			endTime := getMatchingEndTime(startTime, s)
 			ft := &filterTime{
 				minTimestamp: startTime,
@@ -1416,6 +1417,8 @@ func getMatchingEndTime(startTime int64, stringRepr string) int64 {
 		tEnd = tStart.Add(time.Minute)
 	case len(timeStr) == len("YYYY-MM-DDThh:mm:ss") && timeStr[len("YYYY")] == '-':
 		tEnd = tStart.Add(time.Second)
+	case len(timeStr) == len("YYYY-MM-DDThh:mm:ss.SSS") && timeStr[len("YYYY")] == '-':
+		tEnd = tStart.Add(time.Millisecond)
 	default:
 		tEnd = tStart.Add(time.Nanosecond)
 	}
@@ -1459,7 +1462,8 @@ func parseTime(lex *lexer) (int64, string, error) {
 	if err != nil {
 		return 0, "", err
 	}
-	return int64(t * 1e9), s, nil
+	// round to milliseconds
+	return int64(math.Round(t*1e3)) * 1e6, s, nil
 }
 
 func quoteTokenIfNeeded(s string) string {
diff --git a/lib/logstorage/parser_test.go b/lib/logstorage/parser_test.go
index 6e8c458a6..824133796 100644
--- a/lib/logstorage/parser_test.go
+++ b/lib/logstorage/parser_test.go
@@ -191,6 +191,21 @@ func TestParseTimeRange(t *testing.T) {
 	f("2023-02-28T23:59:59", minTimestamp, maxTimestamp)
 	f("2023-02-28T23:59:59Z", minTimestamp, maxTimestamp)
 
+	// _time:[YYYY-MM-DDTHH:MM:SS.sss, YYYY-MM-DDTHH:MM:SS.sss)
+	minTimestamp = time.Date(2024, time.May, 12, 0, 0, 0, 333000000, time.UTC).UnixNano()
+	maxTimestamp = time.Date(2024, time.May, 12, 0, 0, 0, 555000000, time.UTC).UnixNano() - 1
+	f("[2024-05-12T00:00:00.333+00:00,2024-05-12T00:00:00.555+00:00)", minTimestamp, maxTimestamp)
+
+	// _time:[YYYY-MM-DDTHH:MM:SS.sss, YYYY-MM-DDTHH:MM:SS.sss]
+	minTimestamp = time.Date(2024, time.May, 12, 0, 0, 0, 333000000, time.UTC).UnixNano()
+	maxTimestamp = time.Date(2024, time.May, 12, 0, 0, 0, 556000000, time.UTC).UnixNano() - 1
+	f("[2024-05-12T00:00:00.333+00:00,2024-05-12T00:00:00.555+00:00]", minTimestamp, maxTimestamp)
+
+	// _time:YYYY-MM-DDTHH:MM:SS.sss
+	minTimestamp = time.Date(2024, time.May, 14, 13, 54, 59, 134000000, time.UTC).UnixNano()
+	maxTimestamp = time.Date(2024, time.May, 14, 13, 54, 59, 135000000, time.UTC).UnixNano() - 1
+	f("2024-05-14T13:54:59.134Z", minTimestamp, maxTimestamp)
+
 	// _time:YYYY-MM-DDTHH:MM:SS-hh:mm
 	minTimestamp = time.Date(2023, time.February, 28, 23, 59, 59, 0, time.UTC).UnixNano()
 	maxTimestamp = time.Date(2023, time.March, 1, 0, 0, 0, 0, time.UTC).UnixNano() - 1