The House Armed Services Committee passed a waiver Thursday that would allow retired Marine Gen. James Mattis to serve as Defense secretary, despite consternation from both the Republican chairman and Democratic committee members that President-elect Donald Trump Donald John TrumpBarr criticizes DOJ in speech declaring all agency power 'is invested in the attorney general' Military leaders asked about using heat ray on protesters outside White House: report Powell warns failure to reach COVID-19 deal could 'scar and damage' economy MORE did not allow Mattis to testify.

The committee voted 34-28 on the waiver, splitting along party lines.

Current law requires Defense secretaries to be out of uniform for at least seven years before serving in the administration; Mattis retired in 2013. The law has been waived once before, for George Marshall in 1950.

Mattis had been scheduled to testify Thursday about civilian control of the military after his confirmation hearing earlier in the day before the Senate Armed Services Committee. But the House committee canceled the hearing Wednesday after being told by the Trump team that Mattis would not testify.

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“Let me be clear: Gen. Mattis was willing and eager to do so,” Chairman Mac Thornberry (R-Texas) said Thursday. “I talked to him personally. He gladly agreed to come answer our questions about the waiver or other topics. On Tuesday night of this week, however, I was informed that the president-elect’s transition team would not allow Mattis to testify after all. I think that is a mistake.”

Still, Thornberry said he supported the waiver so that Mattis can be confirmed as Defense secretary shortly after Trump’s inauguration.

“I believe we should approve the exception today that allows Gen. Mattis to serve as secretary of Defense so that there is no gap in that important office and so that the nation can benefit, once again, from the service of this extraordinary leader, thinker and public servant.”

On Wednesday, the Trump team said Mattis will work with both the House and Senate if confirmed.

"Gen. Mattis' current focus is on following the constitutional process for confirmation by the United States Senate and testifying at his confirmation hearing of the Senate Armed Services Committee," spokeswoman Alleigh Marré said in a statement. "If confirmed, he looks forward to working with both the Senate and House Armed Services Committees, which play critical roles in supporting our forces and ensuring civilian control of the military.”

Democrats, though, refused to vote for the waiver until Mattis testifies before the committee, saying allowing Trump to bypass the panel threatens to make it irrelevant.

“I’m very disappointed with where we’re at,” said Rep. Adam Smith David (Adam) Adam SmithWhen 'Buy American' and common sense collide Overnight Defense: Marine Corps brushes off criticism of Marines' appearance in GOP convention video | US troops injured in collision with Russian vehicle in Syria | Dems ask for probe of Vindman retaliation allegations Democrats press Pentagon watchdog to probe allegations of retaliation against Vindman brothers MORE (D-Wash.), ranking member of the committee. “The incoming president’s team has decided that the House Armed Services Committee is irrelevant. What I think we should do is say that’s unacceptable.”

Smith also listed a number of other objections he has with the waiver, and several other committee Democrats echoed him. First, it doesn’t name Mattis specifically, only saying that it applies to the first Defense secretary confirmed after passage. The waiver for Marshall specifically named him.

Second, they said they would like to see Mattis exempted from the Uniform Code of Military Justice, the rules that govern behavior in the military, even after retirement. Marshall's 1950 waiver exempted him from the code, and not following suit would mean that Mattis could theoretically be court-martialed as Defense secretary.

Third, they said, despite the committee holding a markup, the full House will vote on the Senate’s bill. That means the name and military justice issues won’t be changed, Smith said.

“If we were doing this properly we could offer an amendment and change that, and we wouldn’t just take the Senate’s language and swallow that,” Smith said.

Republicans who spoke expressed firm support of the waiver, though some acknowledged Mattis’s testimony would have been preferable.

“On January the 20th, the men and women in uniform in the United States need a secretary of Defense,” Rep. Bradley Byrne (R-Ala.) said. “I hear nothing but the greatest of praise of Gen. Mattis from people on both sides of the aisle.”

The full Senate passed the waiver 81-17 on Thursday, too. The full House is expected to take it up Friday.

— Kristina Wong contributed.