Kahraman Sadikoglu and captain Ahmet Yurtdas are believed to have been kidnapped on 16 December after leaving the southern Iraqi city of Basra.
It was not clear who was holding the men and there was no mention of any demands.
"Today is 23 December. We were captured four or five days ago," Sadikoglu said on the tape, released by Turkey's Ihlas News Agency and broadcast on Turkish television.
"We're fine and they will check us out, what we're doing here, and will hopefully release us. God is greatest."
"We don't have any problems with the Iraqi government - we are creating jobs and food for the Iraqis by clearing harbours" of sunken ships, Sadikoglu said in the video, aired by private NTV television. "If that is a crime, too, then we will accept the punishment.
"We have no bad intentions. Their examinations will take a few more days," Sadikoglu said.
"We don't have any problems with the Iraqi government - we're creating jobs and food for the Iraqis by clearing harbours. If that is a crime, too, then we will accept the punishment"
Well-known Turkish ship owner
CNN-Turk television, another broadcaster that aired the video, said the voices of Turkish-speaking men were heard in the background, suggesting that Turkish-born fighters who have joined Iraq's armed opposition might be involved in the capture of the men.No kidnappers were seen in the video and no statement was released by the hostage-takers. No sign or banner was seen behind the two men as in other videos of foreigners taken hostage in Iraq.
Turkish Foreign Minister Abdullah Gul said on Friday that a total of 74 Turks have been killed in attacks in Iraq since the war began.
Some Turkish newspapers speculated that Sadikoglu might have been kidnapped to prevent him from bidding on a multimillion-dollar contract to salvage ships sunken during the Iran-Iraq war in the bay of Basra.
In the video, Sadikoglu said he was working for the United Nations and the interim Iraqi government.
Sadikoglu says he is working for
the UN and Iraqi government
Sadikoglu looked calm, but said Captain Ahmet was "demoralised". The captain did not speak on the video. "We're pretty good. They are taking good care of us," Sadikoglu said of their captors.
Sadikoglu assured their families they would be released soon. "We did not do anything wrong. We did not commit any mistakes."
Sadikoglu is well known in Turkey for salvaging ships around the world and renovating luxury yachts, including the Savarano, a luxury yacht once used by Mustafa Kemal Ataturk.