The Justice Department overrode the earlier recommendation of up to nine years of a prison sentence for Roger Stone, Trump's longtime ally.
Murkowski does not think the president or the Justice Department should have weighed in.
The controversy has also triggered fresh scrutiny from Democrats over the role of Mr Barr, the Justice Department's top official, who has previously been accused of acting in a partisan way to protect Mr Trump.
"I doubt that would do much", said Mitt Romney, the only Republican senator to vote to remove Trump from office in the impeachment trial.
The DOJ's transfer to head in opposition to their very own workforce, and the following resignation of all 4 prosecutors from the court cases, precipitated Trump critics to lash out at Attorney General William Barr and the Trump management for interfering within the legal case.
What he wants to figure out this time is whether the President influenced the Justice Department's recommended sentence for Trump's friend, Roger Stone.
Justice officials insisted the timing was coincidental; they'd already been planning to pull the recommendation.
Now the president is attacking the judge overseeing the case on Twitter.
The exchanges prompted outrage from Democrats, with Senate Minority Leader Chuck Schumer calling on the DOJ inspector general to investigate, and for the Senate Judiciary Committee to hold a hearing.
Stone was convicted of seven crimes including obstruction of justice, lying to Congress and witness tampering in November.
The ball is now in the court of Judge Amy Berman Jackson, who is expected to sentence Stone on February 20.
On Monday, prosecutors recommended to a federal judge that Stone, 67, be sentenced to a prison term of seven to nine years, based on the government's assessment of his conduct under federal sentencing guidelines.
Upset with the department's fresh recommendation, the four prosecutors handling the case withdrew on Wednesday, with one resigning from his position altogether. She also suggested President Trump and his supporters are racist and praised the investigation conducted by Special Counsel Robert Mueller, which ultimately led to Stone's prosecution. Stone has denied wrongdoing and called the case politically motivated. The gulf between the prosecutors and their Justice Department superiors burst into public view the week before Mr.
Grant Smith, one of Stone's lawyers, told Reuters the defense team was examining jurors' social media posts.
"The prosecutors who have now resigned did a masterful job of laying out every element of every charge, backed with ample evidence", Hart, a former Democratic congressional candidate, wrote on Facebook.
"Trump is going around getting even with people".