The White House will not allow senior Trump adviser Stephen Miller, the architect of the administration's latest immigration overhaul and Homeland Security reorganization, to testify before the House Oversight Committee. Committee Chairman Elijah Cummings requested last week that Miller appear before the committee on May 1 to discuss immigration.

White House Counsel Pat Cipollone sent a letter to Cummings Thursday informing the committee that Miller would not testify, but that the administration was willing to make other officials available to the committee. The letter was first reported by the Washington Post.

A senior White House official told CBS News that the administration has offered up "cabinet secretaries and other agency leaders" to discuss immigration in front of various congressional committees. The official also pointed to precedent established by both previous Republican and Democratic administrations who also denied requests for White House staffers to testify.

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In his letter requesting Miller's presence, Cummings said that he wanted the senior adviser to testify "because it appears that you are one of the primary moving forces behind some of the most significant — and in my view, troubling — immigration policies coming out of the Trump White House."

Miller has taken a hard line on immigration, and has recommended some of the administration's most controversial practices, such as separating families at the border. He was also the driving force behind a recent shakeup at the Department of Homeland Security which resulted in the resignation of Secretary Kirstjen Nielsen and other top officials. Because he is not a cabinet official, he is not accountable to Congress in the way that others in the administration may be.

The White House's refusal to allow Miller to testify is the third time in a week that the Trump administration has stymied an effort by Cummings to call officials to testify before the committee. John Gore, the principal deputy assistant attorney general for the Justice Department's Civil Rights Division, defied a congressional subpoena to appear before the committee on Thursday without counsel present. Cummings called Gore to answer questions about his role in the Trump administration's efforts to add a question on citizenship to the 2020 census.

Cummings also said Wednesday that he will schedule a vote on whether to hold a former administration official in contempt of Congress after he failed to appear for a hearing. He had subpoenaed former White House Personnel Security director Carl Kline to appear for a deposition with committee staff Tuesday. But Kline -- at the administration's direction -- didn't show up.

Fin Gomez contributed to this report.