The al-Qaeda-led Islamic State in Iraq has meanwhile claimed that al-Baghdadi was alive. The group said its spokesman was "martyred" in a clash with the "enemies of God".
"We assure the nation that our leader ... Abu Omar al-Baghdadi, may God save him, is basking in the blessings of God among his kin in the Islamic State in Iraq," it said in a statement posted on a website used by Iraq armed groups.
Al-Jubouri was suspected to be behind the kidnappings of Jill Carroll and Tom Fox in Iraq.
"We killed him ... west of Taji on the first day of May," Caldwell told a news conference, referring to a town north of the capital Baghdad.
Carroll, a journalist with the Christian Science Monitor newspaper, was abducted in January 2006 and held for 82 days before she was released.
Christian peace activist Fox was kidnapped in November 2005 and his body was found in March 2006.
Caldwell said al-Jubouri, whose body had been identified through DNA tests, had also been involved in the kidnapping of two Germans, whom he did not identify but said were captured in 2006.
"When we can pick up someone like that who has that kind of history in being associated with the kidnapping and killing of foreign nationals in this country, that's significant," he said.
But Caldwell had no information on the reported death this week of al-Baghdadi.
Hussein Kamal, Iraq's deputy minister of interior, had earlier said al-Baghdadi had been killed in a gun battle with Iraqi and US forces north of Baghdad.
"If that person even exists, again we have nobody in our possession, or know of anybody that does either, alive or dead that is going through any kind of testing or analysis at this point," Caldwell said.
Kamal had earlier told Reuters: "He died as a result of wounds sustained in clashes. The interior ministry has his body to carry out further checks".
Iraqi state television broadcast images of the body of a man it identified as al-Baghdadi. The body lay inside a wooden coffin on the back of a truck, its head badly swollen and bruised.
Caldwell also failed to authenticate claims that Abu Ayyub al-Masri, the leader of al-Qaeda in Iraq, had also been killed.
He said the US military had information.