"They are hoping to cause members of the coalition to decide that the pain and the ugliness and the difficulty of the task is simply too great," he said during a stop at a desert airbase north-west of the capital.
"They know they cannot defeat us militarily. But they are hoping they can win the test of wills. It's a battle of morale. It's a battle of perception," declared Rumsfeld, whose visit comes about three weeks before the US presidential election.
Rumsfeld, who held separate meetings with US commanders, US Ambassador John Negroponte and interim Iraqi Prime Minister Iyad Allawi in Baghdad, arrived just a few hours after two blasts brought more bloodshed to the capital.
The first explosion was near the oil ministry and a nearby police academy soon after 7am. Ministry spokesman Assem Jihad said 17 people had been killed by a suicide car bomb that may have gone off before it reached the academy, where recruits were lining up.
"Most of the dead were passers-by, including seven women," Jihad said.
An interior ministry official said investigators were still trying to decide if the blast was caused by a bomb or a rocket. He put the death toll at six. Police put it at nine.
In eastern Baghdad, the US military said a suicide bomber attacked a US convoy, wounding an American soldier who later died. Two civilians were also wounded. The ministry official said the bomber's charred body was found inside his vehicle.
Insurgents and militants trying to undermine the US-backed government have mounted frequent bomb, rocket and mortar attacks on state buildings and Iraqi security forces.
They have also kidnapped scores of foreigners and Iraqis.
Iraqi kidnappers have released 10 Turkish hostages they had held for over a month after their Turkish employer said it would leave Iraq, Al Jazeera television said on Sunday.
"A statement sent to Al Jazeera said the release came after their Turkish company announced it would stop its activities and completely withdraw from Iraq," the Arab broadcaster said.
Iraqi kidnappers have promised to free two Lebanese men taken hostage west of Baghdad last month, their company's lawyer said on Sunday.
Charbil Karam al-Hajj and Aram Nalbandian disappeared on a road near Falluja on about September 18, along with their Iraqi driver, Ahmad Mirza.
The Pentagon and the interim government are eager to improve security throughout the country before the January polls for a national assembly and prevent insurgents from derailing them.