But Tillerson did say he would not support a "blanket-type" ban on all Muslim immigration into the United States.

Trump has regularly floated using a registry to track Muslims in America as a way to protect the country against potential acts of terror. But his staff regularly tries to tamp down those concerns in statements.

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“I would need to have a lot more information around how such an approach would even be constructed,” he said.

“If it were a tool for vetting, it obviously extends to other groups as well that are threats to the U.S.”