Ross said he plans to meet with Martin on Wednesday at an undisclosed location and that he has been in touch with the tackle through text messages.
"I look forward to that meeting. I think that can help us move forward," Ross said. "I'd like to hear from him what had happened, why he felt that way and what we did and what we could have done to prevent something like this from happening. I want to hear the circumstances, the facts."
The owner vowed before Monday night's game between the Dolphins and Tampa Bay Buccaneers to get to bottom of the allegations and create a locker room culture that "suits the 21st century."
"It couldn't have been a worse nightmare," said Ross, who was joined at the press conference by team president and chief executive officer Tom Garfinkel.
The NFL is investigating Martin's allegations against teammates, including Richie Incognito. Martin, 24, is with his family in California to undergo counseling for emotional issues. Incognito, 30, has been suspended indefinitely.
A special investigator for the league will determine whether Incognito harassed Martin, and whether the Dolphins mishandled the matter.
"We simply don't know what happened or didn't happen yet," Garfinkel said. "We want to know the truth."
Ross strongly endorsed second-year Dolphins coach Joe Philbin, saying he had the "utmost confidence" in the man he hired in 2012. The owner, however, did not express support for beleaguered general manager Jeff Ireland.
"Joe Philbin is probably one of the most organized people I've ever met," Ross said. "When I interviewed him that stood out, but what also stood out was his character. I don't think there is a better person, a more respected person, a more caring person in the National Football League than Joe Philbin."
Ross said to he has formed an independent advisory group that includes Tony Dungy, Don Shula, Dan Marino, Jason Taylor and Curtis Martin to review organizational conduct policies and to make recommendations on areas for improvement.
"We need to look at ourselves. We have to examine everything internally," Ross said. "This is so appalling to me. I know I'm capable of overreacting. I want to get everybody's feedback because we all know the football locker room is a different workplace than most of us are accustomed to. I don't want to make any excuses."
Neither Ross nor Garfinkel addressed an ESPN report that Martin is likely done for the season and feels he cannot return to the Dolphins.
Martin's agent Kenneth Zuckerman did not respond to a request for comment from The Associated Press.
Ross said he will take an "open mind" going into his meeting with Martin.
"I want to hear the facts," the owner said, adding that he'd also like to meet with Incognito.
"He deserves to be heard," Ross said of the suspended guard.
The 6-foot-5, 312-pound Martin left the team two weeks ago. His attorney has alleged that Martin was harassed daily, and Incognito acknowledged leaving a voicemail for Martin in April in which he used a racist term, threatened to kill his teammate and threatened to slap Martin's mother.
Ross's reaction as the scandal mushroomed?
"I was appalled," the owner said. "I think anybody would be appalled. When you first read that text that was reported, to me I didn't realize people would talk or text or speak that way to people."
Incognito is white and Martin is biracial. Teammates both black and white have said Incognito is not a racist, and they've been more supportive of the veteran guard than they have of Martin.
The 6-3, 319-pound Incognito has long been labeled one of the NFL's dirtiest players with a reputation for out-of-bounds behavior off the field. But this season he was a member of the player leadership council, raising questions about the role of Philbin, his staff and Miami management in the case.
The scandal is the latest public-relations headache for Ross since he became majority owner of the Dolphins in 2009. They've endured four consecutive losing seasons, their longest such streak since the 1960s, and often play in a half-empty stadium, their local popularity eclipsed by the Miami Heat.
Ross apologized to Dolphins fans "for being in this position. I know we will come out of this as a better organization."
AP NFL website: http://www.pro32.ap.org
AP Sports Writer Steve Wine in Miami contributed to this report.