U.N. Secretary-General Ban Ki-moon urged Russia and the United States on Sunday to cooperate in rooting out terrorism and said he would unveil a comprehensive plan to fight extremism and violence early next year.

"All these terrorists and ideology extremists should be defeated in the name of humanity," he said at the annual East Asia Summit, this year hosted by Malaysia.

"In that regard, we need to unite. We need to show global solidarity to address ... the common enemy of ISIL, Daesh, some other extremists and terrorist groups," he said, referring to Islamic State.

U.S. President Barack Obama said at the same summit the United States and its allies would not relent in the fight to combat Islamic State extremists and would hunt down their leaders and cut off the group's financing.

"Destroying (Islamic State) is not only a realistic goal, we're going to get it done," he told a news conference after the summit.

"We will destroy them. We will take back land they are currently in, take out their financing, hunt down leadership, dismantle their networks, supply lines and we will destroy them."

Obama said it "would be helpful" if Russia directed its focus on tackling Islamic State and he hoped Moscow would agree to a leadership transition in Syria that meant its president stepping down.

Russian Prime Minister Dmitry Medvedev said countries with large populations of Muslims, including Russia, should unite to fight against Islamic State.

"We need a consolidated anti-terrorist position of those countries that have a large Islamic community, and incidentally Russia is one of these countries," Medvedev said at the annual East Asia Summit hosted this year by Malaysia.

Medvedev said "it is now clear we can only fight this threat by bringing our forces together and by working through such international institutions as the United Nations".

The U.N. Secretary-General said he "highly commended the leadership of the Russian Federation together with the United States to address some of the roots causes of terrorism".

Ban said the United Nations is now gathering ideas and experience from its member states. "Early next year, the U.N. is going to present a comprehensive plan of action to defeat violence and extremism."