The commission that investigated the 11 September 2001 attacks on the US recommended the change, but CIA and Defence Department leaders insist they are not convinced of the need.
They say CIA paramilitaries and military special operations forces each have distinct capabilities but work well together. There are also some things that only the CIA can do, they say.
"I would not accept that recommendation," acting Director of Central Intelligence John McLaughlin testified to senators recently. "I think we have a perfect marriage now of CIA and military capabilities. CIA brings to the mix agility and speed. Military brings lethality."
The September 11 Commission had argued that having two such organisations within the government was redundant.
Paramilitary operations include
training pro-US rebel forces
"Whether the price is measured in either money or people, the United States cannot afford to build two separate capabilities for carrying out secret military operations, secretly operating standoff missiles and secretly training foreign military or paramilitary forces," the report said.
"The United States should concentrate responsibility and necessary legal authorities in one entity."
The commission described a CIA plan in early 1998 to go after al-Qaida leader Usama bin Ladin using operatives from the spy agency and the military. The plan was ultimately cancelled after senior CIA officials and some military officers registered concerns about the risk to US forces and civilians.
Paramilitary operations include training pro-US government or rebel forces, destabilising governments and organisations through violence, and direct attacks on enemy targets and people.
Such operations sometimes are overseen by the CIA and sometimes by special military units such as the Green Berets.
Which operation is used depends on the situation, the need for secrecy and the number of people required.
The CIA's paramilitary force was small before September 11, but has expanded rapidly since. The military's Special Operations Command numbers 49,000 people, including reservists, support personnel and 3000 civilians.
One key distinction between the two is how they are ordered into action.
Special operations troops are subject to the military chain of command, and also to various laws and international treaties governing the use of armed forces.
For the CIA paramilitaries to go into action, the president must sign a secret document called a "finding" that governs their activities, and designated congressional leaders are informed.
Rumsfeld has said CIA engages in
activities that defence should not
Thus, those forces are used more often when secrecy is paramount.
McLaughlin says the CIA director also has broader authority than the military to buy equipment to support paramilitary operations, because the agency can avoid the competitive bidding process to get gear to the field quickly.
Defence Secretary Donald Rumsfeld is also cool to the idea of putting all paramilitary operations under his department's control.
"There are clearly things that the Central Intelligence Agency does that are covert that the Department of Defence ought not to do," he said.
General Richard Myers, chairman of the Joint Chiefs of Staff, said: "There is not a lot of enthusiasm at this point for that kind of change," suggesting there is a limit to what uniformed US military personnel should be allowed to do.
The CIA's paramilitaries are part of the agency's covert operations arm, called the Special Activities Division. Some unit members specialise in propaganda and economic and political disruption. Others, members of the Special Operations Group, participate in combat.
Unlike the Green Berets, the CIA officers can operate without uniforms or identification as US government employees. If any are caught or killed, the government can plausibly deny involvement.
The paramilitary force has been heavily used in Central America, Angola and Afghanistan, among other places.