The local sheriff's office tasked with investigating the Nancy Guthrie abduction is firing back at Kash Patel after the FBI director ripped them for their handling of the case.

Patel went on the "Hang Out with Sean Hannity" podcast and claimed Pima County Sheriff Chris Nanos benched the FBI for the first four days of the investigation. Patel also took issue with Nanos sending critical evidence to a lab in Florida instead of the FBI lab in Quantico.

In response, the Pima County Sheriff’s Office tells TMZ … "Sheriff Nanos responded to the scene the night of the incident, providing immediate local leadership and oversight. A member of the FBI Task Force was also notified and present at that scene, working alongside our personnel. The FBI was promptly notified by both our department and the Guthrie family. While the FBI Director was not on scene, coordination with the Bureau began without delay."

The Pima County Sheriff's Office adds ... "Decisions regarding evidence processing were made on scene based on operational needs. The laboratory utilized by the Pima County Sheriff’s Department and the FBI Laboratory in Quantico have worked in close partnership from the outset and continue to collaborate in the analysis of evidence."

Patel stressed the case was in Sheriff Nanos' jurisdiction and Nanos had the right to call the shots ... but he hopes local law enforcement won't ice out the feds in other cases.

Nancy went missing on February 1, and after dozens of dead ends and tons of media coverage, there's been virtually no progress in the case.

The Pima County Sheriff's Offices tells us ... "We remain committed to a thorough, coordinated, and fact-based investigation and will continue working closely with our federal partners as the process moves forward."