The FBI is sending a stern warning after the arrest of Meghan Markle‘s estranged father, Thomas Markle Sr. … declaring anyone who preys on children will have nowhere to hide.

FBI Director Kash Patel addressed the 82-year-old’s arrest Friday, accusing Thomas of targeting innocent children and vowing to use every resource available to bring alleged predators to justice.

Patel said the bureau worked with law enforcement partners in Los Angeles, Florida, Mexico, the Philippines, and the Marshall Islands to track down evidence and arrest Thomas at his senior living facility in Lakeland, Florida.

And the allegations are disturbing … according to federal prosecutors, investigators searched two Los Angeles-area storage units Thomas had rented since 2008, recovering roughly 78 items, including photographs allegedly showing him with nude underage girls.

Authorities say a witness identified Thomas in two images depicting an adult man with a naked prepubescent girl … while another image showed a nude young girl in what appeared to be a motel room in the Philippines.

First Assistant U.S. Attorney Bill Essayli called the allegations “extremely serious” and vowed to prosecute Thomas to the fullest extent of federal law.

As TMZ previously reported … Thomas was already under investigation in the Philippines after his son, Thomas Markle Jr., claimed he discovered thousands of child sexual abuse images among his father’s belongings.

The FBI previously told TMZ it would assist Philippine authorities and investigate any possible violations of U.S. law … and Friday’s arrest marks a major development in that investigation.

Thomas, who has vehemently denied the allegations in the past, is charged with one federal count of possession of child pornography and faces up to 20 years behind bars if convicted.