US Defence Secretary Jim Mattis said Tuesday that the Islamic State group is "on the run" in Iraq and that security is returning after a four year battle against the jihadists.
As Iraqi forces battled the group inside its northern stronghold of Tal Afar, having ousted it from second city Mosul in July, Mattis visited Baghdad for a day of talks with Prime Minister Haider al-Abadi and top military officials.
"Cities have been liberated, people freed from ISIS, from Daesh," Mattis said, using alternative names for IS.
"The economy is recovering, Iraq is reengaging with the region, and ISIS is on the run."
The jihadists have not been able "to stand up to our team in combat, and they have not retaken one inch of ground that they lost," he said.
US military officials said the new offensive in Tal Afar is proceeding "according to plan".
Iraqi troops backed by coalition air strikes broke through IS defences on the edge of the city Monday night.
Iraqi and coalition aircraft have launched dozens of strikes on the city, where IS fighters have had three years to build up their defences.
Mattis said that despite taking heavy casualties during the nine-month siege of Mosul, Iraqi forces had gained confidence from their victory and were seeking to speed up counter-IS operations.
"It's not over yet, there's hard fighting ahead. They are aware of this and committed to it. They want to accelerate it," he said.
General Stephen Townsend, commander of the US-led operation against IS in Iraq and Syria, said the jihadist group's command and control structure had been significantly disrupted.
"Our coalition operations have freed five million people from the clutches of ISIS, and so far they have not retaken any of that land," he said.
After talks in Baghdad, Mattis flew to Erbil for talks with Iraqi Kurdish leader Massud Barzani as the autonomous Kurdistan region prepares for an independence referendum.
The US and coalition partners are strongly opposed to the poll, slated for September.
"Our point right now is to stay focused like a laser beam on the defeat of ISIS and to let nothing distract us," Mattis said ahead of the meeting.