Oscar Suarez, 32, and Magdalena Devil, 24, both from New Jersey, rented the waterbike June 24 on Holetown Beach but have not been seen since.
discovered a Jet Ski with the registration number 162H, matching the one the couple rented, Roy Morris, the spokesman for Barbados Prime Minister Mia Mottley, said in a statement.
There was no sign of Suarez and Devil, authorities said.
The Nation News reported Mottley met last week with the families of the couple and said they could return to the island at the government's expense over the next year while the case remained open.
The Jet Ski operators contacted the Royal Barbados Police Force after the couple did not return June 24 after the 30-minute rental period. Crews ended their search after nearly a week.
Reynaldo Huaman, Suarez's cousin, told the North Jersey Record last week the couple had been together for about a year.
"The family's obviously still holding out the hope that we find some clues, some lead that gives us some sense of where they could have gone," Huaman said. "Anything that may tell us anything about their whereabouts."
A GoFundMe page was started by the family to help with expenses for the search. The page said the families planned to hire a private investigator.