Some of the worst scenes were in the area around Jablanica, a town on the main route between the cities of Mostar and the capital, Sarajevo, about 70km (40 miles) to the north-east.
A number of other people have been reported missing and a state of emergency has been declared.
Development minister Vojin Mijatovic said the country had witnessed a terrible disaster and appealed for calm.
Officials from the Herzegovina-Neretva Canton said 13 deaths had been confirmed in the area, rather than 16 as earlier reported.
In the town of Fojnica, three other deaths were confirmed.
Search and rescue work continues, with ten people still unaccounted for in Herzegovina-Neretva Canton.
Rivers burst their banks after an overnight storm and aerial photos showed many towns and villages left inundated.
Roads, bridges and railway tracks were washed away or blocked by debris, while landslides left houses buried in rocks and earth as high as their upper storeys.
The main M-17 route, which runs alongside the River Neretva was covered in debris close to Jablanica and a 17km-stretch of railway was badly damaged between nearby Ostrozac and Grabovica to the west. One 200m stretch of track was left hanging in the air by a landslide close to the river south of Jablanica.
The local authority in Herzegovina-Neretva Canton warned drivers to avoid dangerous roads around Jablanica.
Further east along the Neretva river, one homeowner told Bosnian media that water had flooded house at 03:30 on Friday and that they barely managed to save their son before escaping to neighbours and seeing their house collapse.
Meanwhile, 20km to the west of the capital around around Kiseljak, a torrent of water flooded the streets, leaving cars submerged.
MNA/
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