The comments were made by Lt-Gen Raymond Odierno, one of the top US commanders in Iraq.
It is the latest in a series of accusations made by the US about the alleged training and arming of Iraqi Shia militiamen by Iran.
The Iranian government has repeatedly denied involvement.
It says it wants stability in Iraq, and blames the violence there on the US-led invasion.
Deadly barrage
“In the last three months, we have seen a significant improvement in the capability of mortar men and rocketeers to provide accurate fire into the Green Zone and other places,” Lt-Gen Odierno told a press conference.
“We think this is directly related to training conducted inside Iran,” he said.
“One of the reasons why we’re sitting down with the Iranian government… is trying to solve some of these problems,” he added.
The US and Iranian ambassadors to Iraq have held two landmarks meeting in Baghdad, the first in almost three decades, to discuss security issues in Iraq.
A rocket and mortar barrage on the Green Zone on 10 July killed at least three people and wounded 18.
A UN report last month said the threat from rockets and mortars to the area had increased, and that the barrages had become “increasingly concentrated and accurate”.
It said that 26 people had been killed by indirect fire there from mid-February to late May.
