GOP presidential candidate Sen. Ted Cruz Rafael (Ted) Edward CruzTrump argues full Supreme Court needed to settle potential election disputes Press: Notorious RBG vs Notorious GOP The Hill's Morning Report - Sponsored by Facebook - Washington on edge amid SCOTUS vacancy MORE (Texas) challenged President Obama on Wednesday for attacking Republicans who oppose plans to admit thousands of Syrian refugees into the U.S.

"It is utterly unbefitting of the president to be engaging in those kind of personal insults and attacks," Cruz said in Washington, D.C., in video captured by NBC News.

"He talked about how he was belittling the Republican field as scared. Well let me suggest something: 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 said.

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Obama has twice lambasted Republicans this week for opposing his plan to admit 10,000 Syrian refugees over the next year. Republicans have argued that terrorists could slip in among the refugees.

During a Group of 20 press conference in Antalya, Turkey on Monday, Obama said it was " shameful " and "not American" to only allow Christian refugees from Syria into the U.S. Cruz and GOP presidential rival Jeb Bush have both focused on Christians.

“The people who are fleeing Syria are the most harmed by terrorism, they are the most vulnerable as a consequence of civil war and strife,” Obama said.

And in Manila, the Philippines, Wednesday morning, Obama again scoffed at Republicans, saying, "Apparently they are scared of widows and orphans coming into the United States of America.

"At first, they were too scared of the press being too tough on them in the debates. Now they are scared of 3-year-old orphans. That doesn’t seem so tough to me," Obama added.