We should not be building fences or walls, but above all we must look at root causes, in countries of origin," said Ban.
At the Security Council, Russian Foreign Minister Sergei Lavrov will chair a debate on terrorist threats amid intense diplomacy over reaching a political solution to the four-year war in Syria.
Russia will propose a UN Security Council resolution on combating terror groups during the meeting, Deputy Foreign Minister Mikhail Bogdanov was quoted as saying by the RIA Novosti news agency.
This year's UN debate kicked off with a public clash between President Barack Obama and Kremlin leader Vladimir Putin over fighting the Islamic State group and the future of President Bashar al-Assad.
At a US-led counter-terrorism summit on Tuesday, Obama bluntly declared that defeating IS jihadists in Syria "requires a new leader," pressing demands for Assad to step down.
A key ally of Syria, Putin used his UN speech to call for a broad coalition against IS that would include Syria's army.
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