Tamila Swigler said the body had not been identified and that rescuers had not yet located the remaining 12 miners.
Officials had reported poisonous gas in the mine.
Swigler said family members gathered in the church near the mine were "breaking down" after the news was broken to them by rescuers. Rescue work was continuing in the mine, she said.
There had been no communication with the miners since they were trapped after an explosion at 6.30am (1130 GMT) on Monday at the Sago mine in central West Virginia.
Rescuers in the United States have moved deeper into a mine shaft in a desperate search for 13 trapped coal miners.
But the prospects of finding anyone alive on Tuesday appeared bleak after holes drilled into the ground yielded deadly levels of carbon monoxide and no signs of life.
In need of miracle
Ben Hatfield, chief executive of mine owner International Coal Group Inc, said: "With each hour that passes, the likelihood of a successful outcome diminishes."
By early evening, Hatfield said, rescuers were three to five hours from reaching the spot where the miners were thought to be.
"May God bless those who are trapped below the earth"
"We are clearly in the situation where we need a miracle. But miracles happen."
The men, trapped by an explosion on Monday morning in the Sago Mine, were believed to be about 3600 metres past the opening of the shaft.
By early evening, about 35 hours after the blast, rescue teams had penetrated 3420 metres, working their way on foot for fear machinery might cause volatile gases to explode.
George Bush, the US president, said the nation was praying for the men, and he offered federal help to bring them out alive. "May God bless those who are trapped below the earth."
Earlier in the day, rescuers drilled narrow holes into the mine, inserted air monitors and found levels of carbon monoxide more than three times the maximum regarded as safe. Carbon monoxide, a by-product of combustion, can be lethal.
"My father and every person who goes into that mine knows what they're doing. I'm sure they found a way to stay safe. I just want to see him again"
Son of trapped miner
Hatfield said it was possible the miners barricaded themselves somewhere and were still alive. But he said: "We are very discouraged by the results of this test."
Also, a camera lowered down a 16cm hole spotted no sign of the miners, and drilling crews pounded on a steel pipe and listened for a response but heard nothing, Hatfield said.
Upon hearing the discouraging news, many family members retreated to the nearby Sago Baptist Church. Hundreds had spent the night huddled in tents or wrapped in blankets in the cool, damp air.
Nick Helms, whose 50-year-old father, Terry, was among the missing, said: "Obviously, it was devastating," but Helms said his father once told him that mine air tests could be deceiving because safer air could be just a short distance away.
"My father and every person who goes into that mine knows what they're doing. I'm sure they found a way to stay safe. I just want to see him again."
At first, rescue crews moved slowly through the shaft, because they had to stabilise it and repair the roof as they went along. But on Tuesday, officials said, the rescuers realised they had no time to waste and abandoned that approach.
The Mine Safety and Health Administration had rescue and safety specialists on the scene, set up a command centre and brought in a robot capable of exploring areas too dangerous for humans.
Bush said the nation was praying
for the trapped miners
But the robot was abandoned after it became bogged down in the mud.
The cause of the explosion about 160km northeast of Charleston was under investigation.
Coal mine explosions are typically caused by build-ups of naturally occurring methane gas.