You can use call files
. Just read: Asterisk auto-dial out.
I have made simple CGI script that called via web server creates call file (remember to use temp directory) and then moves it to /var/spool/asterisk/outgoing
and Asterisk do rest of the work. From user perspective it works as you described. Also remember to normalize phone numbers (on my web pages they can have spaces, hyphens etc, while in call file they must look as dialable numbers).
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