"Iran still smuggles equipment and aid to terrorists across the border," the general said.
"I find Iranian influence in Iraq unhelpful accross all domains — political, military, economic," he added.
"The Iranians also continue to train special group leaders and provide them opportunities to come back to Iraq."
Special groups is the term US commanders use to refer to Shiite militia factions that have refused to join the political mainstream and which they hold responsible for many of the reprisal killings carried out during the sectarian bloodshed of 2006 and 2007.
Jacoby said that the infiltration of men and materiel by Sunni Arab insurgents from Iraq's western neighbour Syria was down considerably on previous years but remained a risk.
"In the past, we had foreign fighters crossing the border through Syria. That has been greatly reduced from hundreds to just a handful," he said.
"It still happens, they're still dangerous and it's still important to improve Iraqi security along the border."
The head of the Baghdad explosives unit, Major General Jihad al-Jaabiri, charged on Wednesday that coordinated bombings which killed 127 people in the capital the previous day were backed by groups based in Syria or Saudi Arabia.
"Neighbouring countries helped them. The operation required lots of funding, which came from Syria or Saudi Arabia," he said.
Iraq also accused Syria of harbouring the masterminds behind previous deadly bombings in the capital in August and October, and last week the US military announced it was providing Baghdad with a 49-million-dollar surveillance system to improve border security.
The system will monitor activity along a third of Iraq's borders with Iran and Syria, which spawn 1,458 kilometres (around 910 miles) and 605 kilometres (375 miles) respectively, the US military training mission said.
