The assessment came on Thursday after the first week of a huge military operation which has seen the heart of Baghdad hit from the sky for the first time since the start of the US-led invasion.
"As of now, attacks have gone down 70 percent," said Brigadier General Martin Dempsey, commander of the US 1st Armoured Division which has been conducting Operation Iron Hammer in and around the capital.
"We are working as hard as possible to keep it this way and bring it to zero," he told a Baghdad news conference.
At one stage resistance attacks climbed to as many as 35 a day.
Dempsey cautioned, however, that the anti-occupation forces should not be underestimated, however haphazard the tactics of its footsoldiers sometimes were.
"The operators are unsophisticated, they wire things together that sometimes work, sometimes not," he said.
"But the leaders have some kind of communication, planning and supplying ability that probably warrants the word sophistication."
The US brigadier said he had no need of extra troops. "This is a fight for intelligence. I have enough soldiers. The bigger issue is - how do we use them?"
Dempsey said he believed there was a relationship between the insurgents and the bombers who have hit not only the capital, but also the northern oil centre of Kirkuk, but added he could not specify its nature.
He has still not been able to establish the connection between those carrying out bombing attacks against occupation troops and loyalists of the former Saddam Hussain regime.
"They go outside and get the foreigners to drive the cars. Whether this is an alliance or a matter of convenience, I don't know."
"I do have evidence that there is a connection over financing and supplies."
The US brigadier defended the massive show of strength put on by his troops around the capital over the past week, which Tuesday night saw the evening festivities of the Muslim holy month of Ramadan punctured by aerial cannon fire in the heart of Baghdad.
Forces under his command had made 20 Apache attack helicopter missions, five helicopter gunship missions and two using A-10 Warthog tank-buster aircraft, he said.
"This is not a show of force. I want the enemy to know that although I am on his turf, I won't let him use it.
"Now the enemy is not sure what he is doing any more and I like that."