President Joe Biden's asking Americans not to jump to conclusions about the man who shot Donald Trump ... urging people not to make assumptions about his affiliations.

POTUS addressed reporters Sunday morning ... confirming he did speak with the former president by phone Saturday night following the shooting -- and he's keeping Trump and his family in his prayers.

As for the shooter ... Biden points out the public knows his name, but not his motives -- and, he's cautioning people to avoid speculating on who the shooter may be aligned with politically.

JB also runs through the steps he's instituting in the aftermath of the attack ... saying he's checking in with the head of Secret Service about security details surrounding the Republican National Convention.

He's also pushing an independent review of the national security at Saturday's rally to determine exactly how the incident went down.

Worth noting ... Biden still hasn't called the shooting an assassination attempt -- once again saying the FBI's still investigating.

Authorities have identified the shooter as Thomas Matthew Crooks ... and, video -- obtained by TMZ -- has captured the moment he opened fire followed by snipers swiftly taking him down.

Despite the shooting -- which also killed a man named Corey Comperatore -- Trump announced Sunday he won't delay his trip to Milwaukee for the RNC.

Biden is scheduled to speak from the Oval Office about the shooting later today.