ST. PAUL, Minn.   — Minnesota’s new Republican Lt. Gov. Michelle Fischbach said Wednesday she’ll reject the job’s higher salary and hasn’t scheduled the constitutionally-required oath of office as she fights to keep her seat in the Senate.

Fischbach’s ascension to Democratic Gov. Mark Dayton’s administration was automatic, laid out in the state’s constitution by her role as Senate president and set in motion by former Lt. Gov. Tina Smith’s appointment to the U.S. Senate. Smith resigned the job at midnight Tuesday, hours before being sworn in to replace Sen. Al Franken.

Though Fischbach confirmed in a Wednesday statement that she had assumed the role, she stressed she was the state’s “Acting Lieutenant Governor” and made clear her top priority was remaining in the Senate even as Democrats aim to force her out.

It’s the latest turn in the fight between Republicans, who are anxious to protect Fischbach and their current two-seat majority in the Senate, and Democrats, who believe Fischbach must leave her central Minnesota district. If Democrats win a Feb. 12 special election in a suburban St. Paul district, Fischbach’s exit could give them a shot at claiming a 34-33 majority.

Fischbach declined to answer questions after a committee hearing at the state Capitol, including why she directed state officials not to pay her the lieutenant governor’s nearly $96,000 salary — more than double her pay as a lawmaker — and why no swearing in had been scheduled. She repeatedly referenced her earlier written statement.