Iraqi security forces are progressing as planned in their battle to recapture Mosul from the Islamic State (IS) militant group but the fighting will get tougher as they approach the city center, a US general said Saturday.

"We are on (a good) timeline and we are fairly confident that the Iraqis are learning every day, and we are fairly confident they are going to continue to progress well," said Brigadier General Rick Uribe, a deputy commanding general for coalition land forces.

The US-led coalition has been providing training and continual air support for Iraqi security forces as they fight to remove IS from the nation, and some of the bloodiest battles have taken place in Mosul since operations began there in October.

The Iraqis have recaptured the eastern side of the former IS bastion and are making inroads into the more densely populated west.

But "make no mistake about it, as we get closer to the center of the city, it just gets tougher and tougher because of the terrain that the Iraqi security forces are about to enter," Uribe told AFP in a phone interview from Baghdad.

The oldest parts of the city are packed with buildings and crisscrossed with narrow streets that will make fighting more intense.

Army Lieutenant General Stephen Townsend, who heads the anti-IS coalition, this week said about 2,000 Islamist militants remain in and around western Mosul.

The coalition and Iraqi air force sometimes strike Islamist militants as they try to flee the city, many of them seemingly headed west toward Tal Afar near the border with Syria.

Uribe said IS retains control of that city.                                                                                        

"There's significant numbers that are still able to defend that city," he said.