ST. PAUL — 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, who formally resigned this week amid a cloud of sexual misconduct allegations.

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.

“My primary focus will continue to be serving the citizens of Senate District 13 in the Minnesota Senate, who elected me to a four-year term,” her statement read.

It’s unclear how Fischbach’s standing as lieutenant governor would be affected if she’s not formally sworn in. While the state’s constitution makes clear that the Senate’s president becomes lieutenant governor in the event of a vacancy, it also requires an oath of office for executive officials.

Democratic Senate Minority Leader Tom Bakk has promised a lawsuit if Fischbach holds both jobs, arguing it’s unconstitutional. In an open letter to Fischbach, he challenged her assertion that she could hold both offices.

“I respectfully ask you to formally acknowledge that you no longer hold the office of state senator for Senate District 13,” he said.

After a months-long court battle between Dayton and top lawmakers over the governor’s veto of House and Senate funding finally concluded this fall, top Republicans tried to avert another messy constitutional dispute. Senate Majority Leader Paul Gazelka pushed for a special session to elevate a Democrat to become lieutenant governor instead, but Democrats wouldn’t agree.

Fischbach has vowed to run for her seat in a special election if she’s forced out, and top Republicans scoff at the idea that Democrats could defeat her and potentially seize control of the Senate. She has held the deeply conservative seat since 1996 and won by more than 37 percentage points in 2016.