The FBI is investigating letters from sick trolls menacing “Today” show co-host Savannah Guthrie with threats about her missing mother — as the feds are pouring resources behind Arizona police desperately searching for the 84-year-old grandmother.

One letter sent to Guthrie was from a nutcase who said he had knowledge of the abduction — but also included a slew of slurs. The writer also made reference to accused murderer Luigi Mangione and the Jan. 6 US Capitol riot, according to law enforcement sources.

And that’s just one of numerous letters that have been emerging since Guthrie’s mother, Nancy, disappeared from her Tucson home Saturday night.

Savannah Guthrie smiling with her mother Nancy.

Savannah Guthrie with her mom, Nancy, in an undated photo.Instagram/savannahguthrie
Nancy Guthrie, mother of "Today" show anchor Savannah Guthrie, smiles at the camera as she sits at a table with Mahjong tiles and a score sheet.
Nancy Guthrie is believed to have been abducted from her Tucson, Arizona, home.Courtesy NBC UniversalOther notes have been sent to news outlets like TMZ and included purported details from inside Nancy’s home, claims about what she was wearing when she was taken — and even multimillion-dollar ransom demands to be paid in bitcoin.

Detectives with the Pima County Sheriff’s Department are leading the investigation, but the FBI has opened up its sprawling resources to supplement the local cops, sources told The Post.

Federal forensics specialists are helping to analyze the purported ransom letters and follow tips outside Tucson, while the bureau has been poring over cellular tower data to see who passed through Nancy’s neighborhood on and around the night she vanished.

Warrants to search Nancy’s digital accounts — which could help track her movements — are also being expedited by the FBI, while its agents have been deployed to circumvent Arizona jurisdictional restrictions and follow up in-person leads, sources said.

Missing person alert for Nancy Guthrie, 84, from Pima County, with physical description and last known location.

Nancy Guthrie’s missing persons poster.

Possible blood spatters on the tiled floor at the front door of Nancy Guthrie's Tucson home.

Spatters of what appears to be blood were found outside Nancy Guthrie’s Tucson home.
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Customs and Border Protection has even joined in — Tucson is just 70 miles from the Mexican border — to provide sniffer dogs for ground searches.

The federal aid comes as President Trump personally affirmed he would provide whatever resources he could to help with the investigation while speaking to reporters in the Oval Office Tuesday.

“I always got along very good with Savannah. Very unusual situation, but we’re going to find out,” said Trump, who has been interviewed by Guthrie in the past.

“I’m going to call her later on. I think it’s a terrible thing,” he said.

Arizona law enforcement have been tight-lipped about who might be behind Nancy’s abduction.

There are no suspects, cops said Wednesday.

“It could be one, it could’ve been more, I don’t know,” Pima County Sheriff Chris Nanos said of possible kidnappers in a CBS News interview Tuesday

Savannah Guthrie and Nancy Guthrie sitting side by side, smiling at the camera.

Savannah Guthrie with her mom, Nancy, in an undated photo. Nancy went missing earlier this week.
savannahguthrie/Instagram
He has also declined to explain what led police to believe a crime had been committed, saying only “something at the home that didn’t sit well” was found.

But footage from NewsNation has emerged showing blood on her front doorstep, corroborating what law enforcement sources previously told The Post about the scene.

There were also signs of forced entry, while items like Nancy’s phone, keys and ID were left behind, sources said.

Nancy was of sound mind when she was dropped off by her son-in-law Saturday around 9:30 p.m., but police explained she had limited mobility and a medical condition that required medication every 24 hours that she could die without.

And she is quickly approaching 96 hours without it if she is not located by Wednesday night.