Sheikh Hamad's comments are seen as significant as Qatar is a key ally of the US and hosts one of its biggest military bases in the Middle East.
He drew attention to the UN Security Council Resolution 1770 on Iraq, adopted on August 10, 2007, which he called "extremely important".
"This resolution has given the UN part of its deserved role in dealing with the tragedy in Iraq," Sheikh Hamad said.
He said the challenge of critical conflicts around the world had become too big for just a single power.
Plea to UN
Sheikh Hamad said: "The UN must be involved in such conflicts, in its capacity as a political entity that embodies the principles of the international community and its aspirations for a legitimate and peaceful existence."
He cautioned against what he called attempts to drag the world into a new Cold War, saying that this could only lead to increased tension and the proliferation of covert activities worldwide.
Sheikh Hamad said this would contradict the movement towards enlightenment and cultural dialogue among the world's peoples.
While underscoring the international community's obligations in Iraq, he said that the main responsibility lay with the country's leaders.
He said they were responsible for ensuring national reconciliation and guaranteeing justice, peace and security in addition to preserving Iraq's sovereignty and territorial integrity.