(CNN) Acting Homeland Security Director Kevin McAleenan threatened to step down this week if he did not get more authority over his agency in response to another attempt by White House senior policy adviser Stephen Miller to dictate agency hiring, The Washington Post reported Friday.

The clash highlights yet another instance of Miller causing tension with his far-reaching influence as a counselor on immigration matters to President Donald Trump.

The private confrontation centered on Miller's advice to Trump that he should pick Mark Morgan -- whom Trump has named to head Immigration and Customs Enforcement -- for commissioner of Customs and Border Protection, and keep current acting ICE Director Matthew Albence in his role, the paper reported.

Three Trump administration officials told the Post that McAleenan informed senior White House officials that he, not Miller, leads the department and that he should have at least a hand in departmental hiring choices. McAleenan met with acting White House chief of staff Mick Mulvaney, the officials said. One Trump aide described the internal turmoil surrounding the issue as akin to an "immigration knife fight."

Three Homeland Security officials told the Post that Morgan will begin as acting ICE director next week, while Albence will return to his role as deputy director of the agency -- a win for McAleenan.

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