Gregory Korte

USA TODAY

NEW YORK — President Obama held a strategy session with his Iraqi counterpart Monday as coalition forces begin an effort to take the Islamic State stronghold of Mosul.

"This is going to be a challenging battle. Mosul is a large city, and ISIL has embedded itself deeply in that city," Obama said after meeting with Iraqi Prime Minister Haider al-Abadi in New York. "It will be a tough fight."

But he said that the close cooperation between U.S., Iraqi and Kurdish forces should lead to quick progress.

And Abadi seemed even more optimistic, saying Mosul could be taken "in the next few months."

"We are going to kick Daesh out of Mosul," Abadi said, using another name for the Islamic State group, "and deal a huge blow to what Daesh believes in. They must be crushed on the ground, and our heroic fighters are doing that."

The northern Iraqi city, once the county's second-largest with more than two million people, has been occupied by the Islamic State for more than two years. Along with the de facto capital in the Syrian city of Raqqa, it's one of two strongholds that the U.S. and allied forces plan to pressure in simultaneous assaults that it hopes will cripple the terrorist group's military power in the region.

U.S.-led coalition plans to pressure ISIL in both Mosul, Raqqa

But Obama said Monday that the mission can't end there. He said the United States needs to be ready to provide immediate humanitarian aid to the city, rebuilding it "in a way that assures not only ISIL does not come back, but that extremist ideology born out of desperation will not return."

Obama's meeting with Abadi was one of several high-level meetings Obama is planning with world leaders in New York this week, as he also addresses the United Nations General Assembly and a related refugee summit.

In an earlier closed-door meeting with Chinese Premier Li Keqiang, Obama discussed the North Korean nuclear threat, climate change, and trade. And in a phone call with President Kenyan Uhuru Kenyatta, Obama talked about refugee issues, terrorism and the upcoming elections.

Later this week, Obama will have meetings with Israeli Prime Minister Benjamin Netanyahu, Nigerian President Muhammadu Buhari, and Colombian President Juan Manuel Santos.