Jeb Bush also sought to revive his struggling campaign by forcefully attacking front-runner Donald Trump.
"You`re not going to be able to insult your way to the presidency," he said.
Mr Trump was on the defensive early in the debate for his proposed ban on Muslims entering the US, saying "We are not talking about religion, we are talking about security."
However the debate quickly expanded to broader issues of foreign policy and national security.
The candidates repeatedly addressed heightened fears of terrorism in the US on the same day an emailed threat shut down Los Angeles` school system.
But they disagreed over the scope of government surveillance and how to end the civil war raging in Syria.
"If terrorists strike again ... the first question will be, `Why didn`t we know about it and why didn`t we stop it?`" said Mr Rubio, taking aim at Mr Cruz who voted to curtail government surveillance powers.
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