(CNN) At least one young woman has accused Jeffrey Epstein of "improper sexual contact" while he was serving a 13-month jail sentence for state charges in 2008 and 2009, according to a lawyer who represents dozens of Epstein accusers.

Bradley Edwards, the lawyer, also alleged during a press conference Tuesday in New York that Epstein had inappropriate contact with some women as recently as 2011.

Edwards was responding to claims made Monday by Epstein's lawyers that Epstein had maintained a "spotless 14-year record," with "meticulous obedience" to the law, since he pleaded guilty to state prostitution-related charges in 2008 and was released from jail.

Last week, federal prosecutors in New York charged Epstein with sex trafficking of minors and sex trafficking conspiracy. He has pleaded not guilty.

His attorneys touted his good behavior in recent years when asking a federal judge to release Epstein to a set of bail conditions that include confinement to his New York mansion and a wearable satellite tracking device. A hearing is set for Thursday.

Edwards alleged that Epstein continued to deceive women into meeting with him and then engaging in unwanted sexual contact during that time.

As part of his state sentence, Epstein was allowed to work for 12 hours a day, six days a week, at an office. It was during one of those times when he was at the office that the alleged sexual contact occurred, Edwards said.

"The information that we've received from victims, including at least one who personally visited him, was that it was not for some business arrangement and it was for, if you're in jail, improper sexual contact," said Edwards.

He added that "more than one person visited him. I don't know of any that were under the age of 18. They believed that they were going there for something other than a sexual purpose and while there, surprisingly to them, the situation to them turned sexual."

Attorneys for Epstein did not respond to a request for comment.

Edwards also suggested he had information about other business associates of Epstein engaging in "improper conduct," but he was not prepared to name them during the press conference.

The lawyer also revealed that he had recently heard from five accusers who alleged they were assaulted in New York. The accusers came forward after the US attorney's office for the Southern District of New York announced charges against Epstein last week.

"We have talked to at least five who were victims in New York," Edwards said. "The allegations here are the same or substantially the same as the allegations in Florida, which is, some recruiter passed out a line to lure them to his mansion. They believed it was for some advancement or opportunity," he said.

New York and Florida are not the only states where Epstein is under scrutiny.

The New Mexico Attorney General's office is investigating allegations that Epstein committed additional sex crimes in the state, where he owns a ranch with a sprawling mansion and private runway south of Santa Fe. Authorities have interviewed at least two individuals who allege they were abused by Epstein, according to Matt Baca, a spokesperson for New Mexico Attorney General Hector Balderas.

Two women have argued in civil court filings that Epstein's alleged abuse occurred at his Santa Fe ranch, in addition to other locations. It's unclear if those women have spoken to New Mexico authorities. Edwards said New Mexico is "one of those places in which we know very little about."

Baca said these interviews occurred roughly within the last four months, and that, since the indictment was filed against Epstein last week, more individuals have come forward with allegations of misconduct taking place in New Mexico.

"At this point, our intention is to share any evidence we gather with the federal government," Baca said. He added that "it's too early to tell" if New Mexico authorities will take any action.

Edwards has represented several Epstein accusers who were underage in 2005 and 2006, when they say they were assaulted in Florida.

At the press conference Tuesday, Edwards sat beside Courtney Wild, an Epstein accuser, who called for other alleged victims to come forward.

Wild was 15 years old in 2003, when, she says, she and a friend were approached to provide massages to Epstein that would later became more sexual.

"This is no surprise that Jeffrey Epstein was also sexually abusing girls in New York," Wild said. "He did it everywhere. And as long as the victims speak up, he isn't going to get away this time."

"If you have already made the decision to come forward, thank you," she added. "If you have not, the time is now."