The Alaska senator also lauded former Defence Secretary James Mattis' condemnation this week of Mr Trump, saying the retired Marine general's letter to The Atlantic denouncing his former boss were "true and honest and necessary and overdue."
Ms Murkowski said she was "really thankful" for Mr Mattis' letter because she has been "struggling for the right words" to express her thoughts on the president's handling of recent events such as the anti-police-brutality protests that have swept the nation in the wake of the death of Minneapolis man George Floyd.
"When I saw General Mattis' comments yesterday I felt like perhaps we are getting to a point where we can be more honest with the concerns that we might hold internally and have the courage of our own convictions to speak up," she said.
Mr Mattis, who resigned from his post last year in protest of the president's abrupt decision to drawn down US forces in Syria, penned a letter in The Atlantic on Wednesday criticising his former boss's militant response to the anti-police-brutality protests throughout the US over the last week.
"Donald Trump is the first president in my lifetime who does not try to unite the American people — does not even pretend to try. Instead he tries to divide us. We are witnessing the consequences of three years of this deliberate effort. We are witnessing the consequences of three years without mature leadership," Mr Mattis wrote.
Mr Mattis also reproached the administration for ordering law enforcement to clear peaceful protesters near the White House on Monday before Mr Trump embarked on a short walk to the St John's Episcopal Church so he could pose in front of TV cameras holding a bible in his right hand. US Park Police fired tear gas, rubber bullets, and flash bang grenades to clear a path for the president's walk to the famed church.
"When I joined the military, some 50 years ago, I swore an oath to support and defend the Constitution. Never did I dream that troops taking that same oath would be ordered under any circumstance to violate the Constitutional rights of their fellow citizens — much less to provide a bizarre photo op for the elected commander-in-chief, with military leadership standing alongside," Mr Mattis said, taking a dig at current Defence Secretary Mark Esper for his participation in Monday's procession.
Mr Esper has sought to distance himself from the photo op on Monday, saying he did not know that was the White House's intended plan.
Ms Murkowski is often cited as one of the most moderate members among the Senate GOP. She was considered a swing vote during the president's impeachment trial in February before ultimately deciding to acquit him on both articles.
"I didn't support the president in the initial election," Ms Murkowski reminded reporters on Thursday. "I work hard to try to make sure that I'm able to represent my state well, that I'm able to work with any administration and any president. He is our duly elected president. I will continue to work with him. I will continue to work with this administration," she said.
Republican Senator Mitt Romney, the only Republican who joined Democrats voting to convict Mr Trump in February, said Mr Mattis' letter was "stunning and powerful."
He added: "If I ever had to choose somebody to be in a foxhole with, it would be with General Mattis. What a wonderful, wonderful man."
While Mr Mattis is one of the most highly respected military veterans and US defence thinkers among Republican lawmakers, his comments are unlikely to spur any sort of mass exodus within the party from Mr Trump.
Several other GOP senators shrugged off Mr Mattis' condemnation of the president, despite declaring their respect for the retired general.
“I respect General Mattis. I’m the son of a Marine myself. It’s just a very difficult moment here. We need the states, local governments, to ensure they are protecting the safety of people and property,” Montana Republican Senator Steve Daines said, HuffPost reported.
Senator Lindsey Graham of South Carolina, one of Mr Trump's closest allies in the chamber, told Fox News that Mr Mattis just doesn't realise how under siege Mr Trump's presidency is from outside forces.
"From the time President Trump wakes up until he goes to bed there's an effort to destroy his presidency," Mr Graham said.
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