WASHINGTON — A divided Senate Judiciary Committee approved the nomination of Senator Jeff Sessions as attorney general Wednesday, despite a fierce pushback from Democrats over President Trump’s firing this week of the Justice Department’s acting chief, who had objected to the administration’s refugee policy.

The action came on a straight party-line vote, with 11 Republicans supporting their former colleague from Alabama and nine Democrats opposing him.

The full, Republican-controlled Senate now appears ready to approve Mr. Sessions’ nomination next week, which would give the Justice Department and its 113,000 employees a full-time boss after a tumultuous few days that called its independence into question.

The judiciary committee vote came two days after Mr. Trump ousted Sally Q. Yates, a holdover from the Obama administration who was acting attorney general. Ms Yates had refused to defend the president’s order on refugees, saying its legality was unclear. The White House accused her of having “betrayed” her department.