Speaking at a security conference in Singapore on Saturday, Rumsfeld said that "if anyone lived in the Middle East and watched a network like the Aljazeera day after day after day, even if he was an American, he would start waking up and asking what's wrong".
"But America is not wrong. It's the people who are going on television chopping off people's heads, that is wrong," he said.
"And television networks that carry it and promote it and jump on the spark every time there is a terrorist act are promoting the acts," he added.
Aljazeera's media spokesman, Jihad Ballout, said that Rumsfeld was mistaken. "Aljazeera has never ever shown a beheading of any hostage," Ballout said.
"While we work hard to give a comprehensive and balanced account of everything that goes on in Iraq - people clearly have a right to know what is happening on the ground - we have never broadcast images of a hostage being beheaded," Ballout said.
"Aljazeera has never ever shown a beheading of any hostage"
Aljazeera media spokesman
He pointed out that beheading videos were readily available on the internet and had made it on to other television networks. "And because of Aljazeera's reputation, people mistakenly attribute the pictures to us."
Rumsfeld has previously voiced his disapproval of Aljazeera due to its coverage of Iraq and its interviews with Arab dissidents.
In September, the US defence chief said that "over and over again we've seen that Middle Eastern television channel Aljazeera that seems to have a wonderful way of being Johnny-on-the-spot a little too often for my taste".
The TV network is banned from reporting in Iraq and Saudi Arabia. Aljazeera's offices in Baghdad and in the Afghan capital, Kabul, have been hit by US bombs.
Washington said the attacks had been accidental and had not targeted the network.
The broadcaster won over millions of Arab viewers before and during the US-led war against Afghanistan and aired exclusive footage of al-Qaida leader Usama bin Ladin following 9/11.