According to the captors, who belong to Shia leader Muqtada al-Sadr's Mahdi Army, the captive is Brigadier Raad Muhammad Khidr - the former director of Baghdad's al-Rusafa police department.
In the videotape, the masked men read a statement calling on the Iraqi interior minister to release all Mahdi Army fighters arrested during recent clashes with US marines in the southern city of Najaf in return for Khidr's release.
Interior Ministry spokesman Sabah al-Khadim admitted a policeman had been abducted from a police station in the capital's Shia stronghold of Sadr City, but said he was "not a high-ranking officer".
If confirmed, the capture would be the first of its kind by the Mahdi Army.
Sadr City curfew
The incident follows the imposition on Monday of a curfew on Sadr City from 4 pm to 8 am.
The Interior Ministry spokesman said "the curfew will continue during this period till further notice".
He added: "The decision was taken after considering the security situation in Sadr City which has been witnessing violence in the last few days."
A dawn-to-dusk curfew has been
imposed on Sadr City in Baghdad
Earlier on Monday, mortar bombs were fired at the district council hall in Sadr City killing four Iraqi security guards and injuring nine other people, including three US soldiers, the US military said.
Abu Muqtada, a local Mahdi Army leader, said the group had fired 10 to 15 mortars at the building.
"As long as we continue to fight with the government, incidents like this will happen," he said.
Also on Monday, Shia leader Muqtada al-Sadr presented an initiative to Iraqi President Ghazi al-Yawir to end clashes in the southern city of Najaf.
It came as US artillery and tank fire, backed by air power, battered the city as Shia resistance fighters fought US troops and interim Iraqi forces for a fifth straight day.
Since the fighting erupted last Thursday, the military estimates more than 360 resistance fighters have been killed.
Shia leader al-Sadr says he is
resisting foreign occupation
The US toll stands at four dead and 19 members of the US-led occupation forces wounded.
But a spokesman for al-Sadr said only 15 militiamen had been killed and 35 wounded, the majority from cluster bombs fired by US troops.
Al-Sadr rejected a call from interim Prime Minister Iyad Allawi on Monday for his forces to quit Najaf, saying he would fight to his last drop of blood against foreign occupation.
Meanwhile, Abd Al-Hadi al-Darraji, spokesman for al-Sadr's office in Baghdad, told Aljazeera "the latest announcements by the so-called prime minister and defence minister prove that the Iraqi government is determined to eliminate the al-Sadr movement".
"However, God's will and our firm stance against the occupation forces and their collaborators oblige us to defend our holy sites, our pride and the independence of our country," he said.
"The latest announcements by the so-called prime minister and defence minister prove that the Iraqi government is determined to eliminate the al-Sadr movement"
Abd Al-Hadi al-Darraji, spokesman for Muqtada al-Sadr
The spokesman told Aljazeera he survived an assassination attempt on Sunday after a TV interview with the Lebanese al-Manar Channel, during which he heavily criticised the occupation forces and the appointed Iraqi interim government.
"In the interview, I criticised the government for all the decisions it made against the people of Iraq. I said the government should dedicate its decisions for the welfare of the Iraqis not that of the US occupation forces," he said.
"And the result was the killing of my cousin Amir Aziz al-Darraji, one of the mujahidin [fighters] in the city, as he was with me in my car."
Although he laid the blame for the death at the hands of Iraq's occupation authorities, no occupation official has responded to the allegations thus far.