"Make no doubt ... Iran has been the principle supplier of weapons, arms, training and funding of many militia groups," he said. "That has not changed."
"A large number of Iranian weapons still exist here in Iraq.
"We do believe there are still individuals who are co-ordinating activities."
Mohammad Ali Hosseini, an Iranian foreign ministry spokesman, urged the Iraqi government not to follow up on the US accusations.
"Since the beginning, the United States has raised baseless accusations against Iran," he said.
Washington has accused Iran of training, arming and funding Shia fighters inside Iraq. In recent weeks, however, US officials have said the Iran appears to have halted the flow of arms across its border into Iraq.
Philip Reeker, a spokesman for the US embassy in Baghdad, said: "It's difficult to read trends in reductions."
"To draw direct lines from that data - to say that there are fewer attacks and conclude that there's a particular reason for it, vis-a-vis Iran's action - that is something we're not yet prepared to do."
Amid the claim of declining violence, the US military said several rockets and mortar barrages hit US bases in Baghdad overnight on Sunday.
|Smith said the fight had not gone away [AFP]|
"The fight we're up against has not gone away," Smith said.
"Today's mortar and rocket attacks demonstrate that the enemy has the capacity to wage violence."
There were believed to be casualties, but no deaths from Sunday's attacks, Smith said.
Al Jazeera's John Cookson reporting from Baghdad said Smith also told journalists about a number of car bombs found "primed and ready to go" in the north of Baghdad on Saturday.
Also on Sunday, a car bomb exploded by the convoy of a senior Iraqi finance ministry official in Baghdad's Karrada neighbourhood, killing at least five people and wounding nine more, security officials said.
Another car bomb killed three policemen in the city of Mosul, besides wounding 16 people.