"I want you to know that I take responsibility for what is happening and I feel a personal sense of failure about it, and that's all I'm prepared to say on this question," Villaraigosa said at a news conference.
Villaraigosa's brother, sister, nephew and two adult daughters from past relationships sat silently near his side as he addressed journalists. Corina and the couple's two teenage children did not attend.
Although Villaraigosa acknowledged that the public had a right to know about his separation, he argued that people were not entitled to "know all of the details" of his personal life.
Pressed on the issue of romantic ties to another woman, he said: "Those kind of questions are inappropriate, and I won't answer them. My family and I have the right during this difficult time to go through this process free of that kind of speculation."
Villaraigosa announced in a terse statement Friday afternoon that he and his wife were separating.
On Monday, Villaraigosa stuck to a careful choreography -- shouldering the stressful situation while praising his wife and looking forward to getting on with the business of governing the city.
Villaraigosa described his wife as "an exceptional human being in every possible sense of the word. She's a strong and vibrant woman; she's an outstanding, outstanding mother. She's an exceptional example for the entire community."
Those who know Corina Villaraigosa said she was emotionally wounded by the breakup and the events that led to it. The couple have yet to file papers seeking legal separation or divorce, but a mayoral aide said it was only a matter of time before they tackled that decision.
If his marriage is indeed over, Villaraigosa will find himself in familiar company: Facing tough questions over private relationships has become almost a rite of passage for politicians in California and elsewhere.
While campaigning for governor in 2003, Arnold Schwarzenegger weathered allegations that he had groped women during his days as a champion weightlifter and Hollywood actor.
San Francisco Mayor Gavin Newsom admitted in February to having an affair with the wife of his campaign manager. A few days later, Newsom, a potential Villaraigosa opponent in the 2010 governor's race, announced that he was being treated for alcohol abuse.
Former New York mayor and Republican presidential candidate Rudolph W. Giuliani, too, famously had an affair in office that ended his long marriage to former journalist Donna Hanover, now a radio host.
Some Los Angeles civic leaders, none of whom would speak on the record for fear of alienating the mayor, voiced anger at Villaraigosa's seeming inability to flatly reject that any infidelity had occurred. Some fretted that the soft-spoken Corina was suffering through yet one more unnerving episode in her marriage.
She filed for divorce in 1994 after it came to light that her husband had had an affair, leading to an extended separation.
Still, some who pay close attention to city politics predicted that the imbroglio would not resonate much beyond the city's political establishment.
In the coming days, Villaraigosa is expected to move out of Getty House, the mayor's official residence in Windsor Square. He will live at the couple's Mount Washington home during a transitional period.
For the time being, Corina and their two children will stay at Getty House, a city-owned building. But at some point, they will leave and the mayor will return.
Villaraigosa said that he and Corina "are each committed to working together to make our kids our No. 1 priority." He was speaking about 14-year-old Natalia Fe and 18-year-old Antonio Jr., who is heading to Princeton University in the fall.
"This was a hard decision," Villaraigosa said of the end of his marriage. "It was not taken lightly; it is a painful time for all of us, but we'll make it together as a family. On my part, I am going to work as hard as I can to be the best father I can and to be the best mayor that I can be."
