An autopsy was underway on Monday to verify the identity of the body, found in a cable duct in the Yale medical school building. Police would not say Monday if they have a suspect, but said that nobody is in custody.
"We're not believing it's a random act" said Officer Joe Avery, a police spokesman. He would not provide any further details, but said no one else is in danger.
The building where the body was found is part of the university medical school complex about a mile from Yale's main campus and is accessible to Yale personnel with identification cards. Some 75 video surveillance cameras monitor all doorways.
"It's a frightening idea that there's a murderer walking around on campus," said 20-year-old Muneeb Sultan, a chemistry student. "I'm shocked that it happened in a Yale building that had key-card access. It's really sad."
Police have not provided any details on the condition of the body found or how the woman died.
A friend said Monday the doctoral student never showed signs of worry about her own personal safety at work, although she did express concerns about crime in New Haven in an article she wrote last year.
"If she was concerned about (it) she would have said something to someone and they would have known," Jennifer Simpson told CBS' "The Early Show." "And Jon (her fiance) would have known, her family would have known, friends would have known."
Simpson called Le, a pharmacology student from Placerville, Calif., friendly and affable to everyone.
"She was a people person," Simpson said. "She loved people. She loved life. We just can't imagine anybody wanting to harm Annie."
Another friend, Laurel Griffeath, echoed those thoughts on NBC's "Today" show.
"I can't even imagine someone mad at Annie, much less wanting to hurt her," Griffeath said.
Police are analyzing what they're calling "a large amount" of physical evidence.
They will not discuss suspects, other than to say Le's fiance is not a suspect and has assisted in the investigation.
Campus officials have said that the security network recorded Le entering the building by swiping her ID card about 10 a.m. on Sept. 8, and have been baffled before Sunday's gruesome discovery that she was never seen leaving.
The university planned a candlelight vigil at 8 p.m. Monday at the Ivy League university. The Yale Daily News says an e-mail to the Yale community invites participants to "bring a candle and join us in solidarity."
Yale President Richard Levin offered support to Le's family and her fiance, Columbia University graduate student Jonathan Widawsky. The couple was to marry Sunday in Syosset, N.Y., on Long Island's north shore.
"The family and fiance and friends now must suffer the additional ordeal of waiting for the body to be positively identified," Levin said.
Le wrote an article that was published in February in the medical school's magazine. The piece, titled "Crime and Safety in New Haven," compared higher instances of robbery in New Haven with cities that house other Ivy League schools. It also included an interview with Yale Police Chief James Perrotti, who offered advice such as "pay attention to where you are" and "avoid portraying yourself as a potential victim."
"In short, New Haven is a city and all cities have their perils," Le concludes. "But with a little street smarts, one can avoid becoming yet another statistic."
Le, who worked in a laboratory in the five-story building's basement, was reported missing Sept. 8. Her ID, money, credit cards and purse were found in her third-floor office.
More than 100 local, state and federal police had been searching the building for days, using blueprints to uncover any place where evidence or Le's body could be hidden.
Investigators on Saturday said they recovered evidence from the building, but would not confirm media reports that the items included bloody clothing.
Authorities also sifted through garbage at a Hartford incinerator Sunday, looking through trash that was taken from the building in the days since Le went missing.
No one answered the door at the Widawskys' gray, ranch-style in Huntington, N.Y. on Monday.
"He is a very nice young man," next-door neighbor George Mayer said of Jonathan Widawsky. "His family, they're all just wonderful people - very, very nice people."
Both families belong to the same temple.
Mayer, whose mother had been invited to the wedding, said he hopes whoever committed the crime "gets justice - that he gets whatever he deserves."
Yale students on Monday called the finding sad, but some said the discovery doesn't make them feel less safe at Yale.
"Obviously it's a city and there are safety concerns," said 18-year-old Peter Spaulding, a student from Maryland. "It can happen anywhere. You have to go on with life."
Law student Lindsay Nash of West Chester, Pa., said she doesn't sense a heightened level of fear on campus.
"There's always an attention to safety here," she said. "I think there's perception that you need to be careful regardless."
Associated Press reporter David Collins in New Haven and Associated Press Writer Frank Eltman in Huntington, N.Y., contributed to this report.