Originally Published: 01 DEC 22 01:48 ET

Updated: 01 DEC 22 16:58 ET

By Jason Hanna, Veronica Miracle, Jason Kravarik and Travis Caldwell, CNN

(CNN) -- After a day of confusing statements, police investigating last month's killings of four University of Idaho students emphasized Thursday they still believe the attack was targeted -- though they haven't concluded "if the target was the residence or its occupants."

The four students -- Ethan Chapin, 20; Kaylee Goncalves, 21; Xana Kernodle, 20; and Madison Mogen, 21 -- were found stabbed to death November 13 in their shared off-campus home in the college town of Moscow, upending a community that hadn't recorded a single murder since 2015.

Thursday's police statement about targeting comes after police corrected a prosecutor's comments on the matter -- and in the process said something that appeared to depart from their previous stance about a case that has put the college town on edge, with no arrests made or any motive announced.

It also comes amid frustration from victims' relatives and some in the community over a sparse release of investigative details and officials' changing characterizations of the case, including authorities backtracking on whether the community still faced a threat.

The latest sequence began Wednesday, when Moscow police released a statement saying the prosecutor in Idaho's Latah County erroneously said this week that "the suspect(s) specifically looked at this residence," and "that one or more of the occupants were undoubtedly targeted."

How definitive the prosecutor's statements were, however, reflected a "miscommunication," Moscow police said in Wednesday's release.

But the release added: "Detectives do not currently know if the residence or any occupants were specifically targeted but continue to investigate."

That was a departure from -- even if not a contradiction of -- what police had been saying: That they believed the attack was targeted.

On Thursday, a police spokesman tried to clear up the issue:

"We remain consistent in our belief that this was indeed a targeted attack but have not concluded if the target was the residence or its occupants," Idaho State Police spokesman Aaron Snell, who also has been speaking for Moscow police, told CNN on Thursday.

Details about the comments police say the prosecutor made, including when and to whom they were given, weren't immediately available. CNN has asked the prosecutor's office in Latah County, where the university is situated, for comment.

Police for weeks have said they believe the attack was targeted but have not offered specifics about why.

On November 15, Moscow police said they preliminarily "believe this was an isolated, targeted attack and there is no imminent threat to the community at large," and that "evidence indicates that this was a targeted attack."

The following day, police backtracked some of that, saying they couldn't actually say whether there was a threat to the public.

Still, as the investigation advanced, authorities publicly maintained investigators believed the killings were targeted, including during a November 20 police news conference.

Local, state and federal law enforcement agencies are still working to determine who is responsible for the killings. At least 150 interviews have been conducted and more than 1,000 tips from the public have been received, police say.

No suspect has been identified and the murder weapon -- believed to be a fixed-blade knife -- has not been found. Authorities said they have not ruled out the possibility that more than one person may be involved in the stabbings.

Students remembered at campus vigil

Wednesday's police statement came on a day the campus community gathered to pay their respects for the slain students.

The university community gathered at the ASUI-Kibbie Activity Center -- also known as the Kibbie Dome -- to honor the lives of the four students. School officials and three of the four families spoke about how the four would be missed after their sudden deaths.

"The circumstances that bring us here tonight -- they're terrible," said Stacy Chapin, the mother of Ethan Chapin. "The hardest part -- we cannot change the outcome."

Madison Mogen and Kaylee Goncalves were friends since 6th grade, Steve Goncalves said.

"They just found each other, and every day they did homework together, they came to our house together, they shared everything," he said. "In the end, they died together, in the same room in the same bed."

"When I look at all of you guys, there's only one way for this to get a little better, to heal a little bit ... you are just going to have to love each other," Goncalves added.

Ben Mogen, the father of Madison Mogen, shared memories of her love for live music, her hard work ethic and how meaningful it was to him that she was able to experience love with her boyfriend.

While it's unclear how long the investigation will take or "the why in this horrific act," the community "will all go through this together," said Blaine Eckles, the university's dean of students.

He also encouraged everyone to "tell the fun stories, remember them in the good times and do not let their lives be defined by how they died, but instead remember them for the joy they spread and the fun times they shared while they lived."

Eckles also reminded students of the different resources available to them, like counseling, and to share their feelings with those around them.

The hours before the attack

Since the discovery of the attack, investigators have built a timeline of the four students' last known whereabouts.

On the night of the killings, Goncalves and Mogen were at a sports bar, and Chapin and Kernodle were seen at a fraternity party.

Investigators believe all four victims had returned to the home by 2 a.m. the night of the stabbings. Two surviving roommates had also gone out in Moscow that night, police said, and returned to the house by 1 a.m.

Police initially said Goncalves and Mogen returned to the home by 1:45 a.m., but they later updated the timeline, saying digital evidence showed the pair returned at 1:56 a.m. after visiting a food truck and being driven home by a "private party."

The next morning, two surviving roommates "summoned friends to the residence because they believed one of the second-floor victims had passed out and was not waking up," police said in a release. Somebody called 911 from the house at 11:58 a.m. using one of the surviving roommates' phones.

When police arrived, they found two victims on the second floor and two victims on the third floor. There was no sign of forced entry or damage, police said.

Investigators do not believe the two surviving roommates were involved in the deaths.

A coroner determined the four victims were each stabbed multiple times and were likely asleep when the attacks began. Some of the students had defensive wounds, according to the Latah County coroner.