Burr, the ranking Republican on the Senate Veterans Affairs Committee, held up Duckworth's nomination last week because he had questions about a confidential financial questionnaire.
The move angered some veterans groups. Duckworth is a National Guard major who lost both her legs when the helicopter she was piloting was attacked in Iraq.
President Barack Obama nominated her to be an assistant secretary of veterans affairs. She ran unsuccessfully for Congress in 2006 and is now the head of veterans affairs for the state of Illinois. Duckworth had been a critic of the Bush administration's handling of veterans care.
Burr said he had asked for a delay in the Senate confirmation vote because of ''discrepancies'' and ''inconsistencies'' in what he said were three different versions of her financial disclosure statement.
He declined to discuss the details, other than saying, ''The math didn't add up.'' Duckworth subsequently provided additional information.