WATERVILLE, Maine — Police in South Carolina have caught and arrested the estranged mother who allegedly kidnapped two of her children on Thursday during a supervised visit. The children are safe, Waterville Police Chief Joseph Massey said Sunday in a statement.

BethMarie Retamozzo, 34, was caught at a rest area on Interstate 95 at about 10:15 p.m. by South Carolina Highway Patrol, the police chief said.

“She was taken into custody without incident and her three children, Joslyn, Joel and a 2-year-old daughter, were with her and are fine,” Massey said.

Senior Trooper Bridget Wyant of the South Carolina Highway Patrol said Sunday that the four were asleep in the car when troopers found them.

Troopers, who were on the lookout for a 1999 Nissan Quest with a New York license plate, discovered the van parked at the rest area at mile marker 47, located along the southbound lane of I-95, she said.

Retamozzo, who was wanted by the Federal Bureau of Investigation for kidnapping, was taken to Colleton County Detention Center in Walterboro on a fugitive from justice charge, Wyant said.

It is expected that she will have an extradition hearing at the Colleton County courthouse, also in Walterboro, sometime soon.

Retamozzo had a supervised visit with her daughter and son, Joslyn Retamozzo, 7, and Joel Retamozzo, 6, on Thursday in the Waterville area, where the children live with their grandparents. She placed the children in her car and didn’t return at the designated time, police have said.

Police used her cellphone records to determine she was heading south. A BOLO, or be on the lookout alert, was issued for her vehicle.

Retamozzo has legal custody of her 2-year-old daughter, and all three children are now in the custody of South Carolina Human Services officials. Waterville police and the Kennebec County district attorney are working on Retamozzo’s extradition with the FBI and South Carolina officials, the press release from Massey and Wyant said.

Retamozzo was charged with two counts of Class C felony criminal restraint by a parent, the Waterville police chief said.

The two older children have been in the court-ordered custody of their grandmother for several years.

The children’s grandmother called police about 8:45 p.m. Thursday to report that Retamozzo had taken the children earlier in the day during a supervised visit, and police obtained an arrest warrant from Kennebec County Superior Court for the alleged kidnapping.

On Friday, the Waterville Police Department enlisted the assistance of the Maine Information Analysis Center, the National Center for Missing and Exploited Children, New York state law enforcement agencies and several other other entities in attempting to locate Retamozzo and her children.

Detective Sgt. Bill Bonney and lead investigator Detective David Caron “worked around the clock to coordinate the efforts of local and state authorities and the FBI along the entire Eastern Seaboard” to find the children, Massey said.

“We are pleased that this case has come to a successful and safe conclusion for all involved,” the police chief said.