"There are millions of peaceful Muslims across the world, in countries like India, where there is not the problems we are seeing in nations that are controlled by al-Qaeda or ISIS, and we should direct at the problem, focus on the problem, and defeat radical Islamic terrorism," 44-year-old Cruz said.
A Senator from Texas, Cruz's popularity in recent week has gained ground but is still far behind Trump, who during the debate reiterated his position of a temporary ban on Muslims entering the United States.
"We're not talking about religion. We're talking about security. Our country is out of control. People are pouring across the southern border. I will build a wall. It will be a great wall. People will not come in unless they come in legally. Drugs will not pour through that wall," Trump said.
"America is at war. Our enemy is not violent extremism. It is not some unnamed malevolent force. It is radical Islamic terrorist. We have a president who is unwilling to utter its name," Cruz said.
Jeb Bush, the former Florida governor who is struggling
"We need to destroy ISIS in the caliphate. That should be our objective. The refugee issue will be solved if we destroy ISIS there, which means we need to have a no-fly zone, safe zones there for refugees and to build a military force," he said.
"We need to embed our troops inside the Iraqi military. We need to arm directly the Kurds. And all of that has to be done in concert with the Arab nations. And if we're going to ban all Muslims, how are we going to get them to be part of a coalition to destroy ISIS?" he asked.
Trump disagreed arguing that his policy is to make US safe and secure.
"I don't want our country to be taken away from us, and that's what's happening. The policies that we've suffered under other presidents have been a disaster for our country. We want to make America great again. And Jeb, in all fairness, he doesn't believe that," he said.
"Air strikes are a key component of defeating them, but they must be defeated on the ground by a ground force. And that ground force must be primarily made up of Sunni Arabs themselves, Sunni Arabs that reject them ideologically and confront them militarily," he said.
"We must win the information war against ISIS. Every war we have ever been involved in has had a propaganda informational aspect to it. ISIS is winning the propaganda war. They are recruiting people, including Americans, to join them, with the promise that they are joining this great apocalyptic movement that is going to defeat the West.
