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(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.

“This was a power struggle between McAleenan and Miller, and McAleenan won,” one senior administration official with knowledge of what transpired told the paper.

DHS did not have comment on the Post’s story when contacted by CNN. The Post said it could not reach Mulvaney for comment, and White House officials told the paper Miller and McAleenan have resolved some of their grievances since the events in question.

CNN has reached out to the White House for comment on the Post story.

Miller has been staking out a claim at the department, having played a key role in former Homeland Security Secretary Kirstjen Nielsen’s departure. Miller deemed her insufficiently tough at stymieing the migrant influx at the southern border, and openly complained about her to Trump. He has since pushed aggressive policies such as having Border Patrol agents assess migrants’ initial claims for asylum – which Nielsen agreed only to pilot in March, partially to pacify Miller.

The President in recent months gave Miller his blessing to lead the administration’s border policies, with Miller “executing his plan,” including an effective overhaul of the department’s leadership, an official told CNN last month.

Trump recently told aides in an Oval Office meeting that Miller was in charge of all immigration and border-related issues in the White House, according to a person familiar with the meeting.

CNN’s Geneva Sands, Priscilla Alvarez, Evan Perez, Jake Tapper, Abby Phillip and Jeremy Diamond contributed to this report.