Try this, It worked for me.
RewriteEngine On
RewriteCond %{REQUEST_FILENAME} !-d
RewriteCond %{REQUEST_FILENAME} !-f
RewriteRule ^(\w+)$ ./index.php?api=$1
RewriteRule ^(\w+)/([0-9]+)$ index.php?api=$1&id=$2
RewriteRule ^(\w+)/([0-9]+)/([a-zA-Z0-9]+)$ index.php?api=$1&id=$2&action=$3