(CNN)A week after Iraq's Prime Minister Haider Al Abadi declared victory over ISIS in Mosul, Iraqi troops are continuing to clear the country's second biggest city of remaining fighters but US and coalition officials are already focusing on the next objectives in the campaign to defeat the terror group.
The next steps in the fight against ISIS
The next major prize being eyed by the coalition is the Syrian city of Raqqa, the would-be caliphate's one-time "capital." Lt. Gen. Townsend told CNN last week that following the capture of Mosul, Raqqa was "now job number one."
Speaking to reporters on Monday Pentagon spokesman US Navy Capt. Jeff Davis called Syria "our biggest focus of effort."
The US and its coalition allies are using artillery and airstrikes to back the Syrian Democratic Forces, a mix of Arab and Kurdish fighters, in their assault on Raqqa.
There are about 55,000 SDF fighters, made up of 31,000 Kurds and 24,000 Arabs, but the coalition says it will primarily be Arab fighters that take part in the battle for Raqqa.
The US-led coalition has trained some 8,000 SDF fighters and US military advisers have accompanied SDF units as they have pushed into the inner areas of Raqqa.
But despite some rapid initial progress, coalition officials have said that the SDF has encountered tougher resistance in recent days.
"The SDF have incurred casualties as they have met some stiffening resistance from ISIS as they move closer into the city center," US Army Col. Ryan Dillon, a spokesman for the coalition, told reporters last week.
Davis said ISIS was mounting a robust defense, using improvised explosive devices, car bombs and drones, but added that the terror group was "struggling to counter the SDF's multiples avenues of advance."
Some reports had suggested that the SDF had paused its push on Raqqa because of casualties. However coalition officials said that this was not in fact the case, with Davis noting the group had gained territory from ISIS over the last 24 hours.
The coalition estimates that the ranks of ISIS fighters in Raqqa has been reduced from 2,500 to 2,000 since the assault began about 40 days ago.
The coalition is also training a "hold-force" to secure Raqqa after ISIS is ejected from the city. A US defense official told CNN that some 250 members of this force had been trained and the goal is that number will reach 3,000.
"Much work remains to be done in Iraq even after the liberation of Mosul," Davis told reporters Monday.
He called Tal Afar, Hawija and the town of Al Qaim in the Middle Euphrates River valley "the three large areas that I would say are still on the to-do list"
The ISIS-held town of Tal Afar is only about 50 miles west of Mosul and Davis said that Iraq's 15th Armored Division is already making preparations to advance on the city.
The coalition estimates that there are about 700 ISIS fighters in Tal Afar.
"The coalition continues to support the (Iraqi Security Forces) as they carry out detailed clearance operations in Mosul and prepare for follow on operations in Tal Afar," Davis said while adding that there was still significant work to do in Mosul.
Davis said that Iraqi soldiers, counterterrorism units and federal police were still performing "detailed clearance operations" of tunnels and caves in Mosul and were "on the lookout for ISIS fighters that are hiding and working to identify explosive devices that could threaten friendly forces and civilians."
Iraqi officials have expressed confidence that they have enough personnel to clear ISIS from Tal Afar and elsewhere in Iraq.
"We have enough forces to liberate what is remaining," Iraq's military spokesman, Brig. Gen. Brigadier Yahya Rasool told reporters at the Pentagon last week.
"There are enemy enclaves in Hawija, enemy enclaves in western Anbar. The Iraqi Security Forces and the coalition have a plan to get after them and we will move with all due speed to do that," Townsend told reporters last week.
Al Qaim is a town in western Anbar province on the Iraq-Syria border that sits along the Euphrates River Valley. It is connected to a swath of territory that ISIS controls in Syria.
The coalition believes that ISIS has about 1,000 fighters in Al Qaim.
Hawijeh is close to the city of Kirkuk, an area currently controlled by US-backed Kurdish Peshmerga forces.
Coalition officials believe that the fewer than 1,000 ISIS fighters left in Hawija are largely isolated.
ISIS is "largely contained in Hawija," Townsend said, adding that they were "contained to the east by the Kurdish defensive line, and contained to the west by an Iraqi defensive line."
Perhaps the most challenging ISIS target will be in the Syrian section of the Middle Euphrates River Valley.
US defense officials have said that they have observed top ISIS officials increasingly abandoning Raqqa for towns and cities further south along the Euphrates River, such as Mayadin and Deir-e-Zor.
The coalition has been conducting numerous airstrikes in the area, killing several ISIS leaders.
Dillon said "the majority" of airstrikes targeting senior ISIS leaders were taking place in that area.
"We do continue to strike the middle Euphrates River Valley and those are deliberate strikes, there's not full-on combat operations going on there," Dillon said.
There are some pro-regime forces fighting ISIS in the area near Deir-e-Zoir but the thousands of ISIS fighters in that area are relatively far from any coalition-backed forces at this point in time, casting doubt on when an offensive could take place there.