Rex Tillerson, Donald Trump’s pick to serve as secretary of state, said on Wednesday that he did not believe the United States should implement a blanket ban against Muslims.

“I think what’s important [is] that we are able to make a judgment about the people that are coming into the country and so I do not support a blanket-type rejection of any particular group of people,” the former Exxon Mobil CEO said during his confirmation hearing.

“Clearly, we have serious challenges to be able to vet people coming into the country,” Tillerson continued, citing global instability, migration and the fact that many refugees do not have documents. “I don’t think we can just close our eyes and ignore that. We have to be very clear-eyed about recognizing that threat and developing a means to deal with it.”

Still, when Sen. Jeanne Shaheen (D-N.H.) asked Tillerson if he supported creating a national registry of Muslims in the U.S., he said he needed more information.

“I would need to have a lot more information around how such an approach would even be constructed, and if it were a tool for vetting, then it probably extends to other people as well, other groups that are threats to the U.S.,” he said.

Sen. Jeff Sessions (R-Ala.), Trump’s pick for attorney general, has also expressed opposition to a Muslim ban. He said on Tuesday that such a policy “would raise serious constitutional problems,” and that he would oppose a blanket ban on Muslims (but not a ban on people from Muslim-majority nations).

John Kelly, Trump’s pick to lead the Department of Homeland Security, said he did not support registering people based on “[ethnicity] or religion” and wouldn’t implement a registry “unless there was some really compelling reason.”

Trump’s own proposals have shifted since his presidential campaign began. In December 2015, he proposed an unequivocal blanket ban on all Muslims entering the United States, but later claimed he only wanted to focus on Muslims coming from countries that had been hostile to the United States.

Some of Trump’s aides support implementing a Muslim registry, and his top advisers have declined to rule it out.

Colin Powell, who served as secretary of state under President George W. Bush, spoke out against a Muslim registry that was implemented at the time, acknowledging that it made it difficult for people who wanted to visit the U.S.