The undocumented Mexican man threatened to shoot the US president, according to the US Department of Homeland Security

US immigration authorities have arrested a Mexican man who allegedly threatened to shoot President Donald Trump, according to the Department of Homeland Security (DHS).

In a press release issued on Wednesday, DHS Secretary Kristi Noem thanked US Immigration and Customs Enforcement (ICE) officers, saying the "illegal alien ... is behind bars."

Earlier this month, ICE received a handwritten letter from 54-year-old Ramon Morales Reyes in which he vowed to "shoot your precious president in (his) head" at one of Trump's rallies. The DHS published an image of the letter, in which Morales blamed ICE for deporting his family and, after threatening to kill Trump, promised to self-deport.

"We are tired of this president messing with us Mexicans - we have done more for this country than you, white people," the letter read.

Morales, who, according to DHS, entered the US illegally at least nine times between 1998 and 2005 and has a criminal record that includes a felony hit-and-run, was arrested the next day and is now awaiting deportation.

Trump survived an assassination attempt when a gunman took shots at him during a campaign rally in Butler, Pennsylvania. The would-be assassin grazed Trump's ear with a bullet, killed a spectator in the crowd behind him, and injured several others.

"This threat comes not even a year after Butler and less than two weeks after former FBI Director (James) Comey called for the President's assassination," Noem said, urging politicians and the media to "tone down their rhetoric."

READ MORE: Trump says ex-FBI director called for his 'assassination'

Earlier this month, Trump accused Comey - a longtime critic - of calling for his assassination in a now-deleted Instagram post. The image showed seashells spelling out "86 47," captioned "cool shell formation on my beach walk."

White House officials and Republicans said the numbers were a coded threat to the 47th US president, with "86" interpreted as slang for "get rid of" or "kill." An investigation is underway. Comey has denied endorsing violence.