diff --git a/doc/muxers.texi b/doc/muxers.texi
index 3f013516b1..b0dc7e6442 100644
--- a/doc/muxers.texi
+++ b/doc/muxers.texi
@@ -741,6 +741,10 @@ Reset timestamps at the begin of each segment, so that each segment
 will start with near-zero timestamps. It is meant to ease the playback
 of the generated segments. May not work with some combinations of
 muxers/codecs. It is set to @code{0} by default.
+
+@item initial_offset @var{offset}
+Specify timestamp offset to apply to the output packet timestamps. The
+argument must be a time duration specification, and defaults to 0.
 @end table
 
 @subsection Examples
diff --git a/libavformat/segment.c b/libavformat/segment.c
index dbcfe898cf..756161fd96 100644
--- a/libavformat/segment.c
+++ b/libavformat/segment.c
@@ -43,6 +43,7 @@ typedef struct SegmentListEntry {
     int index;
     double start_time, end_time;
     int64_t start_pts;
+    int64_t offset_pts;
     char filename[1024];
     struct SegmentListEntry *next;
 } SegmentListEntry;
@@ -91,6 +92,7 @@ typedef struct {
     int  write_header_trailer; /**< Set by a private option. */
 
     int reset_timestamps;  ///< reset timestamps at the begin of each segment
+    int64_t initial_offset;    ///< initial timestamps offset, expressed in microseconds
     char *reference_stream_specifier; ///< reference stream specifier
     int   reference_stream_index;
 
@@ -644,7 +646,7 @@ static int seg_write_packet(AVFormatContext *s, AVPacket *pkt)
     SegmentContext *seg = s->priv_data;
     AVFormatContext *oc = seg->avf;
     AVStream *st = s->streams[pkt->stream_index];
-    int64_t end_pts = INT64_MAX;
+    int64_t end_pts = INT64_MAX, offset;
     int start_frame = INT_MAX;
     int ret;
 
@@ -694,7 +696,7 @@ static int seg_write_packet(AVFormatContext *s, AVPacket *pkt)
         seg->is_first_pkt = 0;
     }
 
-    if (seg->reset_timestamps) {
+    /* todo: reindent */
         av_log(s, AV_LOG_DEBUG, "stream:%d start_pts_time:%s pts:%s pts_time:%s dts:%s dts_time:%s",
                pkt->stream_index,
                av_ts2timestr(seg->cur_entry.start_pts, &AV_TIME_BASE_Q),
@@ -702,15 +704,16 @@ static int seg_write_packet(AVFormatContext *s, AVPacket *pkt)
                av_ts2str(pkt->dts), av_ts2timestr(pkt->dts, &st->time_base));
 
         /* compute new timestamps */
+        offset = av_rescale_q(seg->initial_offset - (seg->reset_timestamps ? seg->cur_entry.start_pts : 0),
+                              AV_TIME_BASE_Q, st->time_base);
         if (pkt->pts != AV_NOPTS_VALUE)
-            pkt->pts -= av_rescale_q(seg->cur_entry.start_pts, AV_TIME_BASE_Q, st->time_base);
+            pkt->pts += offset;
         if (pkt->dts != AV_NOPTS_VALUE)
-            pkt->dts -= av_rescale_q(seg->cur_entry.start_pts, AV_TIME_BASE_Q, st->time_base);
+            pkt->dts += offset;
 
         av_log(s, AV_LOG_DEBUG, " -> pts:%s pts_time:%s dts:%s dts_time:%s\n",
                av_ts2str(pkt->pts), av_ts2timestr(pkt->pts, &st->time_base),
                av_ts2str(pkt->dts), av_ts2timestr(pkt->dts, &st->time_base));
-    }
 
     ret = ff_write_chained(oc, pkt->stream_index, pkt, s);
 
@@ -793,6 +796,7 @@ static const AVOption options[] = {
     { "individual_header_trailer", "write header/trailer to each segment", OFFSET(individual_header_trailer), AV_OPT_TYPE_INT, {.i64 = 1}, 0, 1, E },
     { "write_header_trailer", "write a header to the first segment and a trailer to the last one", OFFSET(write_header_trailer), AV_OPT_TYPE_INT, {.i64 = 1}, 0, 1, E },
     { "reset_timestamps", "reset timestamps at the begin of each segment", OFFSET(reset_timestamps), AV_OPT_TYPE_INT, {.i64 = 0}, 0, 1, E },
+    { "initial_offset", "set initial timestamp offset", OFFSET(initial_offset), AV_OPT_TYPE_DURATION, {.i64 = 0}, -INT64_MAX, INT64_MAX, E },
     { NULL },
 };
 
diff --git a/libavformat/version.h b/libavformat/version.h
index fd00994134..55e5f4c137 100644
--- a/libavformat/version.h
+++ b/libavformat/version.h
@@ -31,7 +31,7 @@
 
 #define LIBAVFORMAT_VERSION_MAJOR 55
 #define LIBAVFORMAT_VERSION_MINOR 12
-#define LIBAVFORMAT_VERSION_MICRO 100
+#define LIBAVFORMAT_VERSION_MICRO 101
 
 #define LIBAVFORMAT_VERSION_INT AV_VERSION_INT(LIBAVFORMAT_VERSION_MAJOR, \
                                                LIBAVFORMAT_VERSION_MINOR, \