Reporter Nikita Stewart explains Thompson's significance in D.C. politics and connections to key figures. (Washington Post illustration; photo of Thompson by Jason Miccolo Johnson)

The investigation into Mayor Vincent C. Gray’s 2010 political campaign may take longer to resolve than prosecutors have signaled in recent weeks, injecting new uncertainty into the District’s unsettled political landscape — and Gray’s political future.

Jeffrey E. Thompson, the D.C. businessman at the center of the investigation, has agreed to an extension of the deadline for law enforcement officials to file charges against him, according to several people with knowledge of the case. The decision opens the door for Thompson, who court records show is the subject of a grand jury investigation, to negotiate with prosecutors.

Thompson is the alleged financier of an off-the-books shadow campaign for Gray (D). The mayor has not been charged and has declined to comment on the allegations, citing the ongoing investigation, but he has denied any wrongdoing.

Prosecutors have appeared to be methodically building a case against Thompson; without identifying him by name, U.S. Attorney Ronald C. Machen Jr. said last month that the case was moving “extremely fast in pace.”

One by one, a series of Thompson’s business associates and a former D.C. Council member have pleaded guilty to federal charges and implicated Thompson in several alleged campaign finance schemes.

But the timeline changed in recent days because of a behind-the-scenes agreement between Thompson and federal prosecutors, according to several people with direct knowledge of the deal. The clock had been ticking for federal prosecutors to decide whether to file charges against Thompson before the statute of limitations expired.

Most white-collar federal crimes carry a five-year statute of limitations, but it is not uncommon for either party to request a waiver. The five-year time limit to bring charges may have been pegged in part to 2008 activities outlined in charging documents. That year, a Thompson associate allegedly gave $14,650 to federal campaigns and committees at the direction of Thompson, who reimbursed the money.

Gray has not said whether he will seek reelection in the Democratic primary, which is less than nine months away. As the investigation has dragged on, potential donors, supporters and other candidates have said they are unsure how to proceed.

Phil Pannell, a veteran political activist in Ward 8, said residents have grown weary of the long-running investigation.

“Most of the people that I speak with say, if the U.S. attorney has something, then he should come forward with it,” he said. “It really is a disservice to the city that it is taking this long. To have this type of ethical cloud over Mayor Gray’s administration, it’s not helpful in the least.”

Pannell also said the unresolved probes have affected next year’s elections, which include a primary scheduled for April 1. “For an election that is nine months away, you should have a lot more energy around it,” he said. “People are hedging their bets because they don’t know what the situation is going to be with Mayor Gray.”

Thompson’s attorney, Brendan V. Sullivan Jr., declined to comment, as did a spokesman for the U.S. attorney’s office.

Thompson’s agreement underscores the unpredictable nature of such investigations. Such legal maneuverings do not necessarily indicate a willingness on the part of the target to cooperate with investigators — or that prosecutors don’t have a strong case. Prosecutors typically agree to such extensions because they offer more time to build a case.

“If you give them more time and you’re able to have a dialogue, you may be able to convince them they shouldn’t prosecute, or you may be able to work out some kind of a resolution short of an indictment,” said defense attorney David Schertler, a former federal prosecutor in the District.

The details of Thompson’s agreement, including its expiration date, have not been made public.

The investigation into the alleged shadow campaign became public in March 2012, when investigators seized documents during a search of Thompson’s home and office. Thompson is the former owner of D.C. Chartered Health Plan. He was the majority owner of the accounting firm previously known as Thompson, Cobb, Bazilio & Associates. For months, prosecutors battled Thompson’s attorney in court over the government’s right to review millions of pages of records seized in the search.

Last July, public relations consultant Jeanne Clarke Harris pleaded guilty to funneling money from businesses owned by Thompson to her friends, relatives and employees, who then made donations in their own names to political candidates. Prosecutors have alleged in court papers that the partnership between Harris and Thompson was designed to avoid contribution limits and reporting requirements and lasted over many years.

In June, a former Thompson employee and a contractor for his firm both also pleaded guilty to participating in a “straw donor” scheme in which employees of the accounting firm or their relatives wrote checks to campaigns for D.C. Council, mayor and Congress to hide that the money had actually come from Thompson.

Last month, former D.C. Council member Michael A. Brown also pleaded guilty to taking bribes from a company he thought was trying to do business with the city. Court filings connected to Brown’s case also revealed that he had admitted accepting an illegal donation from Thompson that was funneled through Harris.

Mike DeBonis and Nikita Stewart contributed to this report.