Police interviewed Rep. Gary Condit's neighbors Saturday to determine whether a missing woman ever visited the congressman's home, according to District of Columbia Police Chief Charles H. Ramsey.

Ramsey also said investigators had also talked with Condit "at least once" this week.

The news comes amid increasing speculation that Chandra Levy, the 24-year-old former Washington intern missing since April 30, may have had a relationship with Condit, her hometown congressman.

Law enforcement sources confirmed they are in possession of several e-mails in which Levy told friends about her relationship with someone connected to Congress, and one e-mail in which she specifically said the man was a member of Congress.

Meanwhile, less than two miles from Condit's Washington home, about 20 people gathered outside Levy's apartment for a vigil. A Jewish prayer was read and aides to Sens. Dianne Feinstein and Barbara Boxer, D-Calif., spoke.

Condit has called Levy "a good friend," and issued a statement Thursday declining to comment further. Last week he denied allegations he was having an affair with Levy.
 
Levy's parents became concerned when the University of Southern California graduate student did not return to her California home to attend her graduation. Police found the young woman's bags packed for her return to the West Coast on their first search of her apartment.

Law enforcement sources said Levy did not appear to have a plane or train ticket to return home, but she did send an e-mail to her mother saying she was not sure which way she was planning to travel.

When Levy's parents began wondering about their daughter's whereabouts, they contacted Condit — for no other reason, they say, than that he was their congressman. On May 7, Condit notified the police that Levy was missing.

But as authorities were seeking information about what happened to Levy, an e-mail surfaced suggesting she was dating someone connected to Congress.

"Everything else here in DC is going good, my man will be coming back here when Congress starts up again, I'm looking forward to seeing him,'' Levy wrote in a Dec. 23 e-mail to a friend, who provided the message to The Associated Press on the condition he not be identified.
 
In the e-mail, Levy said she misled another friend about the relationship.

"Don't tell her who I am seeing, since" she "thinks that I am dating an FBI agent (which is obviously not the case but I lied to her so she wouldn't ask any questions)," the e-mail states.

A friend of Levy, Jennifer Baker, says Levy told her in November that she had a boyfriend in the FBI.

The Washington Post on Friday quoted Assistant Police Chief Ronald Monroe as saying Levy had visited Condit's apartment "more than a couple of times." Condit is among the witnesses who have been questioned by police.

The conservative, 53-year-old Democrat — a father of two whose wife lives in California — is known for his love of motorcycles, rock music and his decision to live in Adams Morgan, a hip, youthful, bohemian Washington neighborhood.

A source close to the congressman, nicknamed "Mr. Blow Dry" by detractors due to his sharp clothes and smooth tongue, said health problems kept Condit's wife at home, and the congressman frequently visits her on weekends.

Levy's parents said they knew their daughter was consulting periodically with Condit about her aspirations of being an FBI agent.

Levy's disappearance so far is being treated as a missing-person case rather than as a criminal matter.

Fox News' Rita Cosby and the Associated Press contributed to this report.