GOP senator knocks Trump: 'Not a fan of governing by tweet'
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“I am not a fan of governing by tweet. I’m just not, and I know that we’re in a different world now and we communicate differently, but in my view there is a seriousness and a professionalism that comes with the executive," she told the Ketchikan Daily News in an interview published Saturday.
Murkowski added while she and Trump disagree on social media, and the president "is able to capture people's attention," some of the "inflammatory rhetoric and the name calling I don’t think is constructive.” 
Trump has stepped up his war of words with the isolated Asian country, including mocking leader Kim Jong Un as "Little Rocket Man," and warning that the regime “won’t be around much longer” if it continues threats against the U.S.
“I told Rex TillersonRex Wayne TillersonBiden looks to career officials to restore trust, morale in government agencies Biden's State Department picks are a diplomatic slam dunk President Trump: To know him is to 'No' him MORE, our wonderful Secretary of State, that he is wasting his time trying to negotiate with Little Rocket Man,” he tweeted on Sunday morning, using his preferred nickname for the North Korean leader. 
Trump enacted unprecedented sanctions last week that target banks around the globe that do business with North Korea. The move came after Congress passed new penalties of its own earlier this year. 
North Korea tested an intercontinental ballistic missile earlier this year that experts warned could be able to reach Alaska. 
She added to the Daily News that she is "worried" that the Republican Party is becoming too exclusive. 
“Well, I am (worried) in the sense that, as a party, I believe we have always been kind of broader and more inclusive of differing views across the spectrum,” Murkowski said. "We seem to be more fractured within our party now than in the big-tent Ronald Reagan days."