In the footage, the man spoke softly and identified himself as Keith Matthew Maupin.
Relatives confirmed the man is U.S. Private Keith Matthew Maupin, who was captured in an attack on a road convoy last week.
The soldier's captors, who did not identify themselves, said he was in good health, and they proposed to exchange him for Iraqi prisoners held by the U.S.-led occupation forces.
In Ohio, a spokesman for Maupin's family said relatives were relieved to see the video footage and that they are praying for his safe return: "We have believed all along that our prayers would be answered. And we ask that you continue to believe in his safe return, believe in the efforts of our military -- as we do right now -- believe in their skill and know-how as we do, and most importantly, believe in Matt Maupin," said family friend Carl Cottrell.
Maupin's home town of Batavia was decked out in American flags and yellow ribbons -- a sign of faith the soldier will come home safely -- as relatives and friends held a vigil.
"On behalf of his mother, his brother Stephen, and his brother Micah, and his sister Leanne, and the rest of his family, we'd like to say, 'Matt, we love you, and we can't wait until we get to hug you again,'" Cottrell said.
Maupin is one of two soldiers missing since their military fuel convoy was ambushed on 9 April near Baghdad.
His capture comes amid a hostage-taking spree that has caught up foreign civilians from more than a dozen countries this month.
At least one of the hostages, an Italian civilian, was killed by his captors.
Two more Japanese hostages were released today in Baghdad.
The two -- a journalist and peace activist -- were released as Japan prepares to welcome home three other civilians who were released on 15 April after spending a week in captivity. Three Czech journalists were also released yesterday after spending several days in captivity.