Former Obama National Security Adviser Susan Rice won't testify before Congress next week, her lawyer informed a Senate subcommittee by letter Wednesday.

Rice attorney Kathryn Ruemmler said in her letter, which was obtained by CBS News, that Rice "respectfully declines Senator Graham's invitation to testify," citing the fact that she had not received a bipartisan invitation from both Sen. Lindsey Graham, the chairman of the Subcommittee on Crime and Terrorism and ranking member Sen. Sheldon Whitehouse, a Democrat.

Ruemmler said that Whitehouse hadn't agreed to Graham's invitation to Rice, "a significant departure from the bipartisan invitations extended to other witnesses."

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She said that Rice would assist Congress with its probe of Russian election interference "because of the important national interests at stake, provided they are conducted in a bipartisan manner, and as appropriate, in classified session."

Graham responded to Rice's decision not to testify in a statement.

"During a press interview, [Rice] denied improperly unmasking the names of American citizens who were surveilled as part of incidental collection," Graham wrote. "Media reports suggest otherwise." He went on to say, "At an appropriate time, I expect we will continue down this path. I hope Ms. Rice will come before the committee – and not just the press."

While she was national security adviser, Rice requested the unmasking of some names in U.S. intelligence reports. Some were involved in the Trump presidential transition. But Rice has denied that she ever requested that a name be unmasked for political reasons. She has also denied being the source of the leak of the identity of then-National Security Adviser Michael Flynn on calls during the transition period with Russian Envoy Sergey Kislyak.

Graham said in his statement that Obama's former DNI, James Clapper and former acting AG Sally Yates will testify about Russian meddling in the U.S. election and what they knew.

CBS News' Julia Kimani Burnham contributed to this report