Teams on the Trinity had shifted their work from a rescue mission to a search for the body of the 26-year-old man, Fort Worth fire department spokesman Kent Worley said.
He described the missing man and a 23-year-old companion, who swam upstream to safety, as inexperienced rafters who "made a major mistake" by venturing onto the flooding river on Friday. Neither man wore a life jacket.
"The water has gone down, but it's still fairly swift," Worley said. "At this point, (searchers are) going up and down the banks and waiting to see of anything turns up."
At least 16 deaths have been blamed on storms and flooding that have plagued Texas since early June.
Rivers in Oklahoma and Kansas have been receding from record flood crests, revealing millions of dollars in damage to thousands of homes and businesses, in addition to the 1,000 or so damaged in Texas. Authorities found the body of a man believed to be the flood's first fatality in Kansas.
In hard-hit Coffeyville, Kan., authorities again restricted access to residents who had been allowed back into their homes earlier in the week because of high levels of fecal coliform bacteria in the floodwater. Emergency workers have reported experiencing rashes and diarrhea.
On Saturday, President Bush issued a federal disaster declaration for Oklahoma, freeing federal funds to aid two counties ravaged by the flooding.
Radar showed the only rain in the region Sunday morning was a few showers over eastern and southern Texas. More storms are forecast this week in North Texas and along the coast, but heavy rain will be localized.
"We are not going to see the widespread flooding we saw in the past few weeks," said Bill Bunting, a meteorologist with the National Weather Service. "But I can't say completely we are out of the woods."