The debate among the 10 candidates took place on the evening of May 3 at the Ronald Reagan Presidential Library and Museum in southern California.
The candidates were united in calling for the United States to continue pushing for military victory in Iraq.
"We must win in Iraq," Senator John McCain (Arizona) said. "If we withdraw, there will be chaos; there will be genocide; and they will follow us home."
Last week, the rival Democratic Party's presidential candidates, in their first debate, called for a quick end to the war.
The Republican candidates also voiced concern about Iran's nuclear program, saying it would be dangerous for the world if Tehran acquired a nuclear weapon. Iran denies trying to make nuclear weapons.
"The reality is the use of military force against Iran would be very dangerous," former New York Mayor Rudolph Giuliani said. "It would be very provocative. The only thing worse would be Iran being a nuclear power. It's the worst nightmare of the Cold War, isn't it? The nuclear weapons in the hands of an irrational person, an irrational force. [Iranian President Mahmud] Ahmadenijad is clearly irrational."
(compiled from agency reports)