Authorities in Aruba believe a missing American tourist is no longer alive and are seeking to extend a detention order for her travel companion as they seek witnesses who will help them build a case against him, a prosecutor on the Dutch Caribbean island said Friday.

Investigators have few witnesses who saw Robyn Gardner and Gary V. Giordano together in Aruba before he reported her missing, said Solicitor General Taco Stein. Giordano has told police she was apparently pulled away by the ocean current as they snorkeled off the southern tip of the island on Aug. 2.

After so many days, authorities no longer believe the 35-year-old Maryland woman could be alive, so they are holding Giordano on suspicion of involvement in her death. Her remains have not been recovered despite a search of more than four days in the sea and on the coastline in the area where she was reported missing.

"As long as we don't have a body, you can question whether or not she is dead," Stein told The Associated Press in a phone interview. "On the other hand, with all the publicity on the case, if she were still alive she would have made herself known."

Other factors also lead to the conclusion she is dead, Stein told reporters later. Police have recovered her passport from her belongings and don't believe she could have left the island by air with a false identity. They have also found no evidence that she left Aruba by boat.

Asked why there is no further search for her remains, the prosecutor said it would be difficult to search without knowing where to look, even on a relatively small island. Aruba is about 75 square miles (193 square kilometers), nearly the size of Baltimore, Maryland.

Giordano, a 50-year-old business owner from Gaithersburg, Maryland, has denied any wrongdoing through his attorney. He initially helped with the search but Stein said he now declines to answer questions from investigators.

Giordano and Gardner, who is from Frederick, Maryland, arrived in Aruba on July 31 and shared a room at a Marriott hotel. Investigators have surveillance tape of them at a restaurant near Baby Beach, not far from where he says she disappeared while snorkeling. But no witnesses saw them go into the water and police have no knowledge of what else they did on the island, Stein said. Investigators have distributed photos of the couple and are hoping anyone who saw them will contact police.

Investigators particularly need details of how the couple behaved together on the island, and whether they seemed close or quarreled. "We have very little information about what they did on the island. The information we have doesn't give us insight into their relationship," Stein said.

Giordano's lawyer, Michael Lopez, has said his client lost track of Gardner while they were snorkeling and is expected to contest the request.

"We feel we have a strong case, but what the judge will think, I don't know," Stein said.

Under Aruban law, which is based on the Dutch legal system, the judge can extend the next detention order for a maximum of eight days at a hearing scheduled for Monday.

After that period, prosecutors could ask a judge to order Giordano held for as long as 60 days while they prepare a case, but that would require more substantial evidence. Charges would be filed at the end of the 60 days if prosecutors take the case to court.

Aruba's system became familiar to many Americans who followed the disappearance in 2005 of Alabama teenager Natalee Holloway. Authorities repeatedly detained individuals suspected of involvement but then later had to release them for lack of evidence. That case was never solved.

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Dilma Arends Geerman contributed from Oranjestad, Aruba.