ORANJESTAD, Aruba -- Aruba's prime minister says solving the Natalee Holloway case is the island's "No. 1 goal."

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Video: Search Continues For Missing American

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Prime Minister Nelson Oduber went on TV Thursday to express support for the family of the missing Alabama teenager and said his government is working closely with U.S. authorities in the investigation.

There are five people now in custody linked to the disappearance of the 18-year-old woman, but prosecutors admit they still don't have a clear picture of what happened. Aruba's attorney general says "all options are open."

Police said one of the three young men arrested Thursday had been with Holloway at her hotel's casino two nights before she disappeared. That 17-year-old boy and two others said Holloway was with them at a bar two nights later, and they dropped her off at her hotel.

Police have impounded a gray Honda. They're trying to determine if there's a connection between the three young men and two security guards also in custody in the case.

Holloway vanished May 30.

Also Thursday, officials from Aruba's Office of the Attorney General defended the delay in arresting the three additional "persons of interest."

The three men arrested by Aruban police early Thursday morning had been detained soon after Holloway's disappearance. Police officials questioned the trio, then released them back to their families.

During Thursday's news conference, Caren Jassen, spokeswoman for the Aruba Attorney General's Office, told reporters the three men had not been arrested earlier because of "technical reasons." She also denied allegations the three had been given preferential treatment due to their families' position on the island.

Jassen declined to elaborate on the evidence against any of the five men now being held in the case. But she did state that there are so far "no indications (Holloway) is not alive.'

The three young men acknowledged partying with Holloway, 18, of Mountain Brook, Ala., before she went missing last week. According to law enforcement sources, they told police that a man dressed in a security uniform approached her as they dropped her off at her hotel at about 2 a.m.

Two of the suspects, identified as Surinamese brothers Satish and Deepak Kaploe, told police Holloway had been drinking and fell down as she got of the car in front of the hotel.

The source said when the third suspect, Dutch citizen Joran Andreas Petrus Van Der Sloot, tried to help her, she refused, saying, "I can stand on my own."

The Surinamese brothers told police, a black man dressed in a black security uniform and carrying a walkie-talkie went up to Holloway, seemingly to offer his assistance. The suspects then drove off and say they did not see Holloway again.

Suspect's Common-Law Wife Suggests Alibi

The common-law wife of one of two men first arrested in Holloway’s disappearance is offering an alibi for her child's father.

Abraham Jones is under investigation for possible murder and kidnapping charges in the disappearance of Holloway. But the woman he lives with said he was home sick on May 29 and 30 when Holloway was last seen.

Cynthia De Graaf said she was with Jones continuously on both days.

A lawyer representing Jones and Nick John, who is also held under suspicion, says he has yet to see any evidence that Holloway is not alive. He also said there's no evidence the two men were involved in her disappearance.

The two men worked as security guards at a hotel near where Holloway was staying.

A judge Wednesday ruled there's sufficient reason to hold the two men on suspicion of murder and kidnapping.

Family Does Not Blame Chaperones

Holloway's aunt said family members don't blame trip chaperones for the girl's disappearance.

Natalee Holloway joined more than 100 classmates and seven adult chaperones on a five-day excursion to the island. Holloway never showed up for the group's return flight.

Her aunt, Marcia Twitty, said the adult chaperones were "incredible, wonderful people." She said, "These were people who knew our kids day in and day out."

Twitty met with reporters Wednesday outside Mountain Brook Community Church. Classmates have been gathering there for daily prayer sessions.

A large display was erected Wednesday morning in front of one entrance to the church showing a picture of Holloway and the words "hope" and "prayer."

Trip Organizer: 'Chaperones Should Not Be Blamed For Disappearance'

Jodi Bearman, who organized the trip for 136 Mountain Brook, Ala., high school graduates, spoke out in defense of the seven chaperones that went with the graduates on the trip to Aruba.

She said that they should not be blamed for Holloway’s disappearance.

"They (the students) sign a waiver, and it basically makes sure it's clear to them that they are responsible for themselves. Chaperones assist in emergencies, but by no means are liable if an accident should happen or anything like that," Bearman said.

According to Bearman, the students are expected to act as adults and the chaperones are not required to baby-sit the students.

“The chaperones intentionally go out at night, and try to go to the places and check on the kids, but by no means are there specific instructions to do so,” said Bearman.

Bearman said that going on this trip is an individual choice made by the students who want to celebrate graduating high school and that it is not a school-sponsored event. She also said this is the third year for this trip and that the last two years were a success.

Although the students are expected to be responsible for themselves, Bearman said she knew that this being their first venture out after high school, chaperones would be needed to supervise. However, she said they fulfilled their duties and that if anyone had seen Holloway get into a car, then the chaperone would have said something.

"Everyone was getting cabs and leaving, and it's actually a busy club. When you're looking to get your cab, you may or may not notice where the next person went," Bearman said. “I can assure you, if a chaperone saw her getting into a car, there is no way she would have gotten into the car."

Chaperones of the trip to Aruba spoke with Holloway’s parents Monday night via a conference call. Bearman said the reason for the call was to make it clear to the chaperones that the family did not hold them responsible for Holloway’s disappearance.