Warning: SESSION variable max_allowed_packet is read-only. -- Also, Cannot set variable `max_allowed_packet`

Hello.

I just changed servers for Drupal 6.16 and now using MySQL 5.0.89-log. When the 'Database tweaks' sub-module was enabled, the following message appeared:

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Warning: SESSION variable max_allowed_packet is read-only. Use SET GLOBAL max_allowed_packet to assign the value
query: SET SESSION max_allowed_packet = 16777216 in /usr/home/foodir/foo/foo2/includes/database.mysqli.inc on line 128

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Another version of the same error message is:

Cannot set variable `max_allowed_packet` to `16777216` in your database configuration!
Probably you do not have proper privileges.
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The server default is max_allowed_packet = 64M. Also, php memory_limit = 64M and max_execution_time = 600 sec. The site is new and there's not a large number of modules, yet especially when compared to what it will be in the future. This error didn't exist with MySQL 4.1 and nothing had been changed since the server switch.

Q: What could be causing this?

Thanks.