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U.S. Rep. Gary Condit

WASHINGTON (CNN) -- District of Columbia police investigating the disappearance of intern Chandra Levy will take up the offer to search the Washington apartment of U.S. Rep. Gary Condit, a police source told CNN.

The decision came after Abbe Lowell, Condit's attorney, made a wide-ranging pledge of cooperation with police, including giving them access to Condit's apartment.

"We are going to take him up on that," the police source said.

Law enforcement sources say Condit, 53, admitted to police in an interview Friday that he had a sexual relationship with Levy. However, police say Condit, a married father of two, is not considered a suspect in the disappearance of the 24-year-old, who was last reported seen April 30 at her gym in Washington.

Lowell's offer of cooperation came as the intense media spotlight on the California Democrat continued, with an attorney for the Levy family charging that Condit has "not been helpful." The family called on him to take a lie-detector test to help determine what happened to Levy.

Levy

Meanwhile, Anne Marie Smith, a United Airlines flight attendant who said she and Condit had a sexual affair until shortly after Levy's disappearance, claims Condit asked her to sign a false affidavit denying their affair and told her that she did not have to disclose the information to FBI agents investigating Levy's disappearance. Smith and her attorney are scheduled to meet with representatives of the U.S. Attorney's office Tuesday in Washington, sources told CNN.

Condit has issued a statement denying that he asked anyone to mislead investigators. His San Francisco attorney, Joe Cotchett, has issued a statement saying the affidavit submitted to Smith was a draft that she was encouraged to edit if she felt it was incorrect.

Family: Condit's credibility 'suspect'

Speaking to reporters on Monday, Lowell said Condit would allow police to search his apartment, question his staff and examine phone records and any other documents police deem relevant. However, he declined to say whether Condit would submit to a lie detector test.

"The congressman wants to see if anything he has, anything he knows, anything he could surmise, could help lead to help finding this missing person," Lowell said.

But in an interview on CNN's Larry King Live, Billy Martin, the attorney for the Levy family, said a lie detector test is necessary because Condit's credibility is "suspect."

"Getting information from Congressman Condit is like pulling teeth. It comes out only when he's forced to admit these facts," said Martin. "The family does not believe that anything short of a polygraph ... would give them any confidence."

Martin said that, in a telephone conversation in early May, days after Levy disappeared, her mother, Susan Levy, asked Condit directly if he had had an affair with her daughter.

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"He lied. He misrepresented his relationship. He told her no," said Martin, who called on Condit to meet with Levy's parents and private investigators they have hired to work on the case.

Lowell said he would be willing to "discuss" any police requests for a lie detector test or DNA sample. But he argued that there is no need for a lie detector test because Condit has cooperated with police and is not considered a suspect.

"The police have said that he's answered all questions to their satisfaction. They have said that he has been cooperative. They have said that they are comfortable with his answers," Lowell said.

"There's no question to test. There's nothing that a lie detector could test. He's not been inconsistent to the police."

'The truth has to come out,' says mother

But Levy's mother said: "Mr. Condit has not been very truthful to me up 'till now. I think that there's things that are unknown, and the truth has to come out."

A Levy family spokesman, Michael K. Frisby, said family members are troubled by statements Condit gave to police about the last time he spoke to Levy.

Law enforcement sources told CNN that Condit acknowledged to police he spoke with the intern by phone April 29. But Frisby said that, in a meeting with the Levy family last month, Condit said his last contact with the former intern took place April 24.

"The family now feels we need to be assured the congressman is telling the truth," Frisby said.

Martin said that in the early days of the investigation, police chased rumors that Levy may have been despondent and could have committed suicide. He said Condit "knew that Chandra was upbeat, he knew that she was in good spirits. We believe that he knew that she was excited -- about what, we're not sure."

"He never corrected the record," Martin said.

Attorney blasts media

In his appearance before reporters Monday, Lowell blasted the media for focusing on Condit.

"Go take your cameras and your pads and your pencils and try to see if there's somebody else out there who might have some information that could actually find this woman, as opposed to prying into the private lives of the Condits," he said.

Lowell said he has sent letters to the heads of major news organizations, asking them to stop staking out Condit's homes in Washington and California, as well as the homes of his children.

"Let them start living their lives again," he said.

In contrast, Martin thanked the media for their attention to the case. "The press has done a very good job in keeping this matter alive. And by keeping this matter alive, it will help us, we believe, to learn where Chandra is or what's happened to her."

Martin's law firm has turned over more than 400 tips to police, Martin said.

Levy had completed an internship with the federal Bureau of Prisons and was preparing to return to California when she vanished. Police are treating her disappearance as a missing persons case and have named no suspects.

Condit is one of roughly 100 people police have interviewed in connection with the case. Others include friends, colleagues and members of the gym where she was last seen.

"Nothing can be ruled out now because, again, you know until we can answer that question of what happened to her and find her one way or the other, we're going to have to continue to trace and retrace steps," Police Chief Charles Ramsey told reporters, adding that a search of landfills is also part of the police probe.

"That's just covering bases and making sure we look at all possibilities," he said.

CNN National Correspondent Bob Franken contributed to this report.