WASHINGTON ( CNN ) -- U.S. Sen. David Vitter returned from a week-long absence from Congress Tuesday , a day after he made a public apology for `` a serious sin '' as investigators probe an alleged prostitution ring that operated in the nation 's capital . Vitter vanished from public view last week after his phone number turned up among those kept by a reputed `` D.C. Madam '' in records that have become part of her upcoming criminal trial . The Louisiana conservative apologized privately to his fellow Republican senators at their weekly policy lunch Tuesday , senators who attended the lunch said . One described Vitter 's his apology as `` humble '' and `` short and to the point . '' The senator said Vitter was met with a great deal of `` empathy '' by the senators in the room . Watch Vitter apologize for his `` past failings '' » . Tuesday morning , Vitter did not visit his Senate office , where the media had camped out in anticipation of his return . He also was not seen at a residential address near the Supreme Court building . He eventually emerged at a scheduled Senate hearing taking place near his office building . He arrived nearly 30 minutes late for the start of the panel , which heard testimony regarding commercial airline service to outlying parts of the United States . At first , only CNN and a local camera crew had learned of his whereabouts . But as word spread among media outlets , Senate officials had to urge order among the gaggle of newspaper writers , photographers and other television crews that began making noisy entrances to record Vitter 's return . The senator left the hearing early and tried to ignore shouted questions and camera lights in the hallway . He then turned and stopped . Vitter referred to comments he made Monday evening near New Orleans , Louisiana , then said , `` I look forward today to be back at work , really focused on a lot of important issues for the people of Louisiana . I 'll leave it at that . '' Last week , Vitter acknowledged in a statement that his number had turned up in the telephone records of accused `` D.C. Madam '' Deborah Jeane Palfrey . Vitter , 46 , said those calls were made prior to his election to the Senate in 2004 , and he and his wife had already dealt with what he termed a `` serious sin '' privately , through marriage counseling and confession to a Roman Catholic priest . On Monday , Vitter and his wife Wendy spoke to reporters in the New Orleans suburb of Metairie , where he lives . `` I know this has hurt the relationship of trust I 've enjoyed with so many of you and that I have a lot of work to do to rebuild that trust , '' the senator said . Palfrey is facing money laundering and racketeering charges stemming from her alleged prostitution operation . She had denied the charges , saying her business was a legitimate , legal escort service . At first she tried to sell the phone records to raise money for her defense . After a judge imposed restrictions on the records , Palfrey distributed the records without charge , hoping media outlets would help track down clients who her lawyer believes may help in her defense . Vitter is the first lawmaker entangled in the case , although State Department official Randall Tobias resigned in May after confirming he patronized Palfrey 's business . Larry Flynt 's Hustler magazine claimed credit for exposing Vitter 's connection to Palfrey , saying he came clean only after a journalist working as a paid consultant for the magazine discovered the senator 's number in her phone records . E-mail to a friend .
NEW : Sen. David Vitter resumes work on Capitol Hill . NE : According to ` ` ' ' , '' he tries to keep low profile . NEW : Conservative talk to fellow Republicans at lunch . NE : Journalists seeking Vitter cause disruption in a committee meeting .