Alabama Sen. Tommy Tuberville rejected a meeting with Defense Secretary Lloyd Austin as the stalemate over the senator’s hold on military promotions continues.

CNN’s Kaitlan Collins reported in a tweet Thursday that Austin reached out to Tuberville’s office after he had made comments earlier this week that he had heard nothing from the Pentagon nor the White House over the military holds he put in place as a protest over the new military policy providing paid leave and travel expenses for servicemembers seeking abortions.

Tuberville’s office responded that the senator declined the meeting, CNN reported.

According to CNN, Tuberville’s office said “he did not have time for a call today or this weekend.” CNN attributed the information as coming from a “senior defense official.”

Related: Top U.S. military leader must step down as Sen. Tuberville continues blocking replacement

“This comes as Tuberville has complained that Austin has not tried to reach him about his hold on military nominations in protest of the Pentagon’s abortion policy,” CNN’s Collins said in a tweet.

Tuberville’s office did not immediately respond to a request by AL.com for comment on the CNN report.

The non-meeting would seem to add another layer on a months-long controversy that has hung over the Senate. Tuberville’s protest does not have the support of Senate leaders Chuck Schumer and Mitch McConnell.

Tuberville has repeatedly said he will maintain his holds until the defense department either cancels the abortion policy or Congress votes its approval. Tuberville has also said that military nominations can go forward on a one-by-one basis for Senate confirmation – a time-consuming process that typically is bypassed by the Senate approving military promotions by voice vote.

President Joe Biden on Thursday continued his criticism of Tuberville’s strategy.

“He’s jeopardizing U.S. security by what he’s doing,” Biden said, according to an Associated Press report. “It’s just totally irresponsible in my view.”

This story will be updated.