"I was obviously very taken aback by it and hurt. I have some processing to do on that end," Kitzhaber said, addressing the allegations for the first time during a televised political debate against a gubernatorial challenger.
"I'm proud of her and I support her. This is now a personal issue and we need time to work through this together," said Kitzhaber, a Democrat seeking re-election in November.
Hayes, the founder of an environmental consulting firm, said Kitzhaber had not known about the marriage until Wednesday, and that he was not present at Hayes' announcement at her request.
Hayes said she deeply regretted her actions. She said she accepted about $5,000 for the marriage, but never lived with the man and met him only a handful of times, adding she had not seen him since they divorced in 2002.
The exchange on the illegal marriage amounted to only a fraction of a wide-ranging debate that also focused on state education funding, same-sex marriage and proposed coal exports, among the issues leading up to the November election.
"This is not something that involves us, it involves Cylvia Hayes and the IRS and the governor," Kitzhaber's Republican opponent, Dennis Richardson, said at the public radio-sponsored debate.

It was unclear how the admission of an illegal marriage will affect the race, in which Kitzhaber seeks an unprecedented fourth term.
Kitzhaber leads Richardson in public opinion polls by nearly 10 percentage points, according to the latest average by Real Clear Politics.