12:03 PM PT -- During his federal court appearance Monday, Judge Ryon McCabe ordered that Ryan Wesley Routh be held without bond until his trial.

Ryan Wesley Routh, the alleged would-be Trump assassin, revealed his lethal intentions in a letter he wrote prior to getting arrested ... according to the Justice Department.

Federal prosecutors released the troubling note Monday, saying Routh wrote about his plans to assassinate former President Donald Trump, and in it, he also calls on others to make attempts on the Republican nominee's life.

The note even promised a hefty monetary reward to whomever finished "the job."

Part of the note reads, "This was an assassination attempt on Donald Trump but I failed you. I tried my best and gave it all the gumption I could muster. It is up to you now to finish the job; and I will offer $150,000 to whomever can complete the job."

Per the Justice Department, Routh penned the letter months ago ... and left it in a box at someone's home. The DOJ says the box also had ammunition and a metal pipe inside of it.

The recipient of the box and the letter, who has not been named by the DOJ, reportedly opened the chilling gift after Routh was named a suspect in the assassination attempt against Trump.

The materials were later handed over to the authorities.

The DOJ says Routh also left a handwritten list in his car which had dates and places where the former prez was set to appear. Authorities say they found 6 cell phones while searching his vehicle ... one of which reportedly had a Google search about traveling from Palm Beach County to Mexico.

The information was released by the DOJ as part of a detention memo ahead of Routh's hearing today ... where Judge Ryon M. McCabe will decide if Routh should continue to be held until his arraignment next week.

As we previously reported, Secret Service spotted an AK-style rifle peeking out from shrubbery only hundreds of yards away from where Trump played golf in West Palm Beach.

After Secret Service shot into the area, authorities say Routh dropped his weapon -- which was never fired -- and fled in a nearby SUV.

He was later stopped by Martin County deputies, who slapped cuffs on him before he was charged with possession of a firearm by a felon and possession of a firearm with an obliterated serial number. Further charges are expected to come as the investigation continues.