In a statement posted on the internet on Monday, the council, which groups eight groups, said: "Your brethren in the military wing of the Mujahidin Shura (consultative) Council abducted the two American soldiers near Yusifiya."
The authenticity of the statement could not be verified.
Some hours after the announcement the US military said it did not give "much credence" to the claim.
One Pentagon official told Reuters: "There's no indication it's an authentic claim. The folks on the ground aren't giving it much credence."
The two soldiers went missing after they came under attack at a traffic control point near the town of Yusifiya, south of Baghdad, on Friday. Another soldier died in the attack.
The US military named the missing soldiers as Kristian Menchaca, 23, and Thomas Tucker, 25.
It also said that three fighters have been killed and seven American soldiers wounded, with 34 people being detained during the search for the two American men.
Major General William Caldwell, a spokesman for US forces in Iraq, said fighter jets, unmanned aerial vehicles and diving teams had been deployed to find the two men missing since Friday.
"We have surged intelligence, surveillance and reconnaissance platforms and employed planes, boats, helicopters and UAVs to ensure the most thorough search possible on the ground, in the air and in the water," Caldwell said in a statement on Monday.
"While searching for our soldiers, we have engaged in a number of significant actions against the anti-Iraqi forces," he said.
He also said the military had received 63 tips and had launched 12 cordon and search operations, eight air assaults and 280 flight hours were logged.
"Approximately 12 villages have been cleared in the area, and we continue to engage local citizens for help and information leading to the whereabouts of our soldiers," he said.