"I would encourage you, Mr. President, come back and insult me to my face", Cruz told reporters outside the Capitol Hill Club in Washington.
"Let me suggest something Mr. President: If you want to insult me, you can do it overseas, you can do it in Turkey, and you can do it in foreign countries".
Obama has ripped those comments, calling them "shameful" and has said the nation should "not have religious test to our compassion".
"Well let me suggest something", Cruz continued.
This afternoon, a visibly angered Ted Cruz lashed out at the President, who is now traveling overseas.
He stated, "If you were Muslim from Syria, you can get into this country...if you were a Christian from Syria it was almost impossible to get in and yet the Christians were having their heads cut off. It's the most unfair thing, this is during the Obama administration...what's wrong with us?"
Obama stepped up his attack on Republicans Wednesday during a stop in the Philippines -- Tuesday night, USA time -- and said they were afraid of "widows and orphans".
Ted Cruz took offense to President Barack Obama's "cheap insults" and challenged him to a debate.
That said, if the senator were serious about a spirited debate over USA refugee policy, perhaps the best course of action would be an argument between this version of Ted Cruzand last year's version of Ted Cruz. "That doesn't seem so tough to me".
"It is utterly un-befitting of a President to be engaging in those kinds of personal insults, attacks", Cruz added. Speaker of the House Paul Ryan announced that a bill demanding a "pause" in Obama's refugees resettlement plan, had strong bipartisan support in Congress and will be voted upon very soon.
"ISIS showed they are committing an act of war against the West", he said, explaining that Republican party leaders had assembled a task force to consider legislation "as quickly as possible" that would suspend the admittance of Syrian refugees.
Republican governors in Alabama, Arizona, Arkansas, Illinois, Indiana, Louisiana, Michigan, Mississippi, Massachusetts, and Texas were among the first to issue statements announcing that Syrian refugees will not be allowed to resettle in their states, MSN reports.