In the message, 31-year-old Mohamed Lahouaiej-Bouhlel "expresses satisfaction at having obtained a 7.65mm pistol and discusses the supply of other weapons", the source said.
The driver, who was shot dead by police after his deadly rampage, took pictures of himself at the wheel that he shared by SMS, the source added.
Over 200 investigators are working on identifying the recipients of the messages, one of the officers told AFP.
Among the six is a 38-year-old Albanian, who was arrested this morning on suspicion of supplying the pistol that Lahouaiej-Bouhlel used to fire at police trying to block his route.
Police later found the gun in the truck, along with two replica assault rifles and a dummy grenade.
Lahouaiej-Bouhlel's estranged wife was released today after two days of questioning.
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