Rumsfeld resigned last month, the day after the Republicans lost control of the US congress with voter frustration over the Iraq war dominating the election.
News of Rumsfeld's trip comes nine days before he is due to be replaced by Robert Gates, former head of the Central Intelligence Agency.
Rumsfeld has come under sharp criticism at home and abroad over his handling of Iraq and the treatment of detained terror suspects. But he defended the US presence in Iraq on Friday in farewell remarks to Pentagon staff.
He said an early US withdrawal from Iraq would be a "terrible mistake" that would threaten the stability not only of Iraq but also the region.
Rumsfeld urged Americans to show patience with the war in Iraq, saying there would be "dire consequences were we to fail here".
Iraq and Afghanistan have made considerable strides, he said, but "those countries are not there yet".
"To pull out precipitously and inject that instability into the situation there in that country, and in that region, I think would be a terrible mistake," he said.