The head of US Central Command in Iraq, Army General Joseph Votel, says between 800 and 900 Islamic State (Isis) fighters have been killed so far in the battle to retake Iraq's second city, Mosul, from the Islamist group.
However military officials believe there are still between 3,000 and 5,000 Isis Jihadists within the city itself, and between 1,500 and 2,000 in other areas just outside the city.
Iraq's military told Washington that 57 Iraqi forces personnel have died in the operation so far. Another 250 people are thought to have been wounded. According to the BBC, Kurdish Peshmerga forces have lost between 20 and 30 fighters so far.
It is unclear how many civilians have died in the attack. There are an estimated 600,000 civilians still inside the city, and fears they may be used as human shields by Isis.
On Wednesday (26 October), US Lieutenant General Stephen Townsend, senior US commander in Iraq, gave details of the fire-power brought to bear in the battle to retake Mosul.
"The coalition has delivered more than 2,100 aerial bombs, artillery and mortar shells, HIMARS rockets and Hellfire missiles since the Iraqis started operations to liberate Mosul on October 17th," said Townsend via video link from Baghdad.
"This relentless campaign of strikes has removed hundreds of fighters, weapons, and key leaders from the battlefield in front of the Iraqi advance."
However, the commander warned that victory could take weeks, possibly months, and that there would be a lot of hard fighting ahead.
Gaining control of Mosul would signal the end of Isis (Daesh) in Iraq, at least in terms of holding significant territory, and the fight would then be taken to the group in neighbouring Syria.
Townsend said Raqqa would represent an even tougher challenge, as unlike in Iraq the country's government wouldn't be an ally and the coalition would leave much of the fighting to "local partners."