CHICAGO — Five months ago, Mayor Kwame Kilpatrick of Detroit and his chief of staff, Christine Beatty, testified that they did not have a romantic relationship. They continued to deny a relationship out of court as well, as they had for several years.

But that was before the Detroit Free Press published a cache of text messages between the two, many of them flirtatious or sexual, and others referring to meetings in hotels.

On Monday, Ms. Beatty resigned her post, saying she could “no longer effectively carry out the duties of chief of staff.”

The resignation came days after a county prosecutor opened an investigation into whether Mr. Kilpatrick and Ms. Beatty may have committed perjury when they concealed their affair during their testimony last summer.

Two city council members demanded an internal investigation into the pair’s relationship, which has outraged voters and led to calls for Mr. Kilpatrick’s resignation. The council is also looking at the city charter, to determine whether he could be forced from office.

One of their chief concerns: whether the 37-year-old mayor intentionally misled the city council into approving an $8.4 million settlement between the city and three former police officers. The men claimed they unfairly lost their jobs because they were looking into potential wrongdoing by the mayor’s security team, which could have exposed the intimate relationship. The political scandal has stunned Motor City, which has lost more population in the last half-century than any other in the country, has a poverty rate that hovers around 30%, and is routinely ranked by the U.S. Census Bureau as one of America’s most impoverished urban centers.

“This is a city whose resources are already limited,” said John Riehl, who heads up the American Federation of State, County, and Municipal Employees Local 207, one of the local groups calling for the mayor to step down. “Is it really any surprise that people are furious?”

Mr. Kilpatrick, who is married and has three children, issued a brief statement to reporters. “These five- and six-year-old text messages reflect a very difficult period in my personal life,” he said. “It is profoundly embarrassing to have these extremely private messages now displayed in such a public manner. My wife and I worked our way through these intensely personal issues years ago.”

In her resignation letter, Ms. Beatty, a 37-year-old mother of two who was married at the time of the romance, said she regretted “the devastation that the recent reports have caused to the citizens of Detroit, to my coworkers, to the mayor’s family, and to my family and friends.”

Neither their attorneys nor Mr. Kilpatrick’s family — including his mother, Rep. Carolyn Cheeks Kilpatrick, a Democrat of Michigan — returned calls for comment Monday.

It has been a rocky political tenure for the man once dubbed “America’s hip-hop mayor.” The two-term mayor, who previously worked as a teacher and served in the state Legislature, won points early in his term for reorganizing the city’s police department and pushing for urban renewal in the downtown area: The mortgage firm Quicken Loans has announced plans to move an estimated 4,000 workers to downtown from a Detroit suburb, and two new casino resorts opened there late last year, creating new service jobs.

But such gains often were overshadowed by Mr. Kilpatrick’s clashes with Detroit’s established political guard, and press reports of questionable charges on a city credit card, and allegations he used city funds to lease a Lincoln Navigator for his family.

Mr. Kilpatrick and Ms. Beatty have known one another since high school and worked closely together during his 2001 successful mayoral bid.