The US military in Iraq has accused Iran of orchestrating an attack that killed five US soldiers and of using Lebanese militants to train insurgents.
Gen Bergner said a veteran Hezbollah man was captured in March
The information came from a top Hezbollah fighter recently captured in southern Iraq, an army spokesman said.
Brig-Gen Kevin Bergner said the suspect admitted working with the Quds Force, linked to Iran's Revolutionary Guards.
Iranian officials have always denied involvement in anti-US and anti-British attacks in Iraq.
Tehran says it supports the US-backed Iraqi government, and blames the violence on the myriad conflicts within the country since US-led forces toppled Saddam Hussein in 2003.
But Gen Bergner insisted that the Quds Force knew of and helped plan the attack on a Karbala government compound in January.
Gen Bergner said the Quds Force and the Iranian-backed Lebanese Shia organisation Hezbollah were jointly operating camps near Tehran in which they trained Iraqi fighters before sending them back to Iraq to conduct attacks.
Gen Bergner said Hezbollah's Ali Moussa Dakdouk - who he said was captured in southern Iraq in March - was the liaison between Iran's shadowy Quds Force and a breakaway Shia group.
Gen Bergner said it was this group - led by Qays al-Khazaali, a former spokesman for cleric Moqtada Sadr - that carried out the attack against the provincial government building in Karbala in January.
Mr Dakdouk "was directed by the Iranian Quds Force to move Iraqis in and out of Iraq and report on the training and operations of Iraqi special groups," Gen Bergner said.
"They were being taught how to use EFPs (explosively-formed penetrators), mortars, rockets, as well as intelligence, sniper, and kidnapping operations," he added.
Correspondents say the accusations appear to be part of a continuing campaign by the US military to link Iran with insurgency violence in Iraq.
US commanders have long accused Tehran of financing and anti-US militants, but this is the first time they have accused Iranians of prior knowledge of the Karbala attack.
Gen Bergner said Mr Dakdouk had told his US interrogators that the Karbala attackers "could not have conducted this complex operation without the support and direction of the Quds force".
Five Americans were killed in the Karbala assault, a bold and sophisticated assault in which up to a dozen gunmen posed as a US security team to gain access to the government compound.
Mr Khazaali and his brother were captured with Mr Dakdouk, Gen Bergner said
Hezbollah officials said they would not comment until they had checked claims that Mr Dakdouk was a member of their group.
Hundreds of US-led forces in Iraq have fallen victims to EFPs. Hezbollah used the same weapons to deadly effect in its conflict with Israeli forces in southern Lebanon in 2006.