I just wrote a program that embeds and uses a GNU-GPL library (GPLv3 or at your discretion any later version).
Can I release my program under the GNU AGPL v3 license?
Yes, you can use a GPL3 library  in an AGPL3 program . You can also cut-and-paste GPL3 code into an AGPL3 program.
Both the ordinary GNU GPL, version 3, and the GNU Affero GPL have text allowing you to link together modules under these two licenses in one program.
Obviously, you should make the code for both portions available from your AGPL program, and include all appropriate copyright notices, as you normally would with GPL/AGPL code.
In fact, you can even use an AGPL library in a GPL program, as long as you make the AGPL code available whenever its conditions are met (e.g. from behind a GPL-licensed content management system).
Notwithstanding any other provision of this License, you have permission to link or combine any covered work with a work licensed under version 3 of the GNU General Public License into a single combined work, and to convey the resulting work. The terms of this License will continue to apply to the part which is the covered work, but the work with which it is combined will remain governed by version 3 of the GNU General Public License.
 Or GPL2+ library or GPL3+ library
 Or AGPL3+ program