General:
* Stating
* Declaring
* Expressing
* Uttering
* Remarking
* Mentioning
* Observing
* Indicating
* Communicating
Informal:
* Telling
* Speaking
* Talking
* Whispering
* Shouting
More specific:
* Affirming (if the speaker is confirming something)
* Asserting (if the speaker is making a strong claim)
* Denying (if the speaker is rejecting something)
* Conceding (if the speaker is admitting something)
* Proposing (if the speaker is suggesting something)
* Explaining (if the speaker is making something clear)
* Arguing (if the speaker is presenting a case)
* Complaining (if the speaker is expressing dissatisfaction)
The best synonym to use depends on the specific situation and the meaning you want to convey.