Texas Sen. Ted Cruz on Wednesday said that if President Barack Obama wants to be critical of his rhetoric, he should "come back and insult me to my face."

Obama has been critical of Cruz's proposal for handling the Syrian refugee crisis, which includes allowing in Syrian Christians, but not Syrian Muslims. The president earlier this week called that approach "shameful," adding, "we don't have religious tests to our compassion."

"Mr. President, if you want to insult me, you can do it overseas, you can do it in Turkey, you can do it in foreign countries, but I would encourage you, Mr. President, come back and insult me to my face," Cruz told reporters Wednesday morning, looking directly into the cameras. "Let's have a debate on Syrian refugees right now. We can do it anywhere you want. I'd prefer it in the United States and not overseas where you're making the insults. It's easy to toss a cheap insult when no one can respond, but let's have a debate."

Those remarks came after Cruz emerged from the Capitol Hill Club flanked by conservative Iowa congressman Steve King, who endorsed his presidential bid earlier this week. The two were meeting with House Republicans, to whom Cruz laid out his campaign strategy in a closed-door meeting.