The article in The New Yorker says Mr Rumsfeld extended a programme already in use in Afghanistan.
The operation encouraged the abuse and sexual humiliation of Iraqi prisoners to gain intelligence, it says.
The Pentagon has described the claims as "outlandish, conspiratorial...filled with error and anonymous conjecture".
"No responsible official of the Department of Defense approved any programme that could conceivably have been intended result in such abuses," a Pentagon spokesman said.
The article was written by distinguished American journalist Seymour Hersh.
It quotes unnamed intelligence officials as saying the original programme gave blanket approval to kill or capture and interrogate "high value" targets in the war on terrorism.
The programme, Mr Hersh says, stemmed from frustrating efforts to capture al-Qaeda leaders after the start of US operations in Afghanistan in 2001.
According to Mr Hersh, commandos were allowed to carry out instant interrogations - using force if necessary - at CIA detention centres around the world.
Denial
Last year, Mr Rumsfeld and Stephen Cambone, his undersecretary for intelligence, expanded the scope of the programme and brought its methods to the Abu Ghraib prison near Baghdad, the article says.
Pictures of inmates being abused by American guards at the prison sparked outrage in the US and beyond.
Mr Rumsfeld and senior Pentagon generals have been grilled by congressional committees.
During the hearings Mr Rumsfeld said that abuse had never been sanctioned by senior commanders, and that the few who had engaged in illegal interrogation methods would be punished.
Seven soldiers have been charged.
Hersh's allegations were rejected by Pentagon spokesman Lawrence Di Rita soon after the article appeared on The New Yorker website on Saturday.
"This story seems to reflect the fevered insights of those with little, if any, connection to the activities in the Department of Defence," Mr Di Rita said in a statement.
The operation encouraged the abuse and sexual humiliation of Iraqi prisoners to gain intelligence, it says.
The Pentagon has described the claims as "outlandish, conspiratorial...filled with error and anonymous conjecture".
"No responsible official of the Department of Defense approved any programme that could conceivably have been intended result in such abuses," a Pentagon spokesman said.
The article was written by distinguished American journalist Seymour Hersh.
It quotes unnamed intelligence officials as saying the original programme gave blanket approval to kill or capture and interrogate "high value" targets in the war on terrorism.
The programme, Mr Hersh says, stemmed from frustrating efforts to capture al-Qaeda leaders after the start of US operations in Afghanistan in 2001.
According to Mr Hersh, commandos were allowed to carry out instant interrogations - using force if necessary - at CIA detention centres around the world.
Denial
Last year, Mr Rumsfeld and Stephen Cambone, his undersecretary for intelligence, expanded the scope of the programme and brought its methods to the Abu Ghraib prison near Baghdad, the article says.
Pictures of inmates being abused by American guards at the prison sparked outrage in the US and beyond.
Mr Rumsfeld and senior Pentagon generals have been grilled by congressional committees.
During the hearings Mr Rumsfeld said that abuse had never been sanctioned by senior commanders, and that the few who had engaged in illegal interrogation methods would be punished.
Seven soldiers have been charged.
Hersh's allegations were rejected by Pentagon spokesman Lawrence Di Rita soon after the article appeared on The New Yorker website on Saturday.
"This story seems to reflect the fevered insights of those with little, if any, connection to the activities in the Department of Defence," Mr Di Rita said in a statement.
