"We feel very positive we can bring this to a peaceful resolution," said Orange County Sheriff Kevin Beary, talking to reporters about five hours after the incident began Thursday afternoon.
Police said Bismark Rodriguez, 39, checked into the Boardwalk Inn, a Disney resort property, Thursday morning with his 4-year-old son.
From his hotel room, he ordered room service and about 2:00 p.m. took hostage the man who delivered his food, police said.
'He's heavily armed'
"All we know is he's heavily armed; he's got at least some handguns and possibly a rifle," Beary said.
Police said earlier that the suspect had threatened to harm himself and the hostages.
Rodriguez told police he wanted to talk to his wife. The couple were in the middle of a divorce, police said.
Officials gathered some family members at the hotel, who they said gave the negotiating team background information on the family's situation. They had not located Rodriguez's wife.
Beary said Rodriguez has had some domestic problems in the past.
Asked if the suspected gunman might be watching television news coverage of the standoff, Beary said, "He's not watching television, 'cause we've done some things so he can't watch television."
Hotel providing counselors to guests
The hotel evacuated guests from at least 40 rooms near Rodriguez's room and sent them to other areas of the sprawling, 910-room hotel complex. Police halted the flow of traffic into the building where the gunman was holed up.
Disney spokeswoman Diane Ledder said evacuated guests had received toiletry bags and could talk with counselors if they needed to.
"We want to make sure that no one's vacation is spoiled because of this incident," she said.
Most of the hotel's operations are continuing as normal, Ledder said, and restaurants and shops on the Boardwalk are open.
The complex is located directly across the street from Disney-MGM Studios, not far from the Epcot Center.
Beary said police SWAT officers had been conducting a demonstration for Boy Scouts nearby when the situation was reported.
"We were right there off (Highway) 417 at the range," he said.
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