Interior Secretary Ryan Zinke called Alaska's senators Wednesday warning them about potential changes to policy after the state's Republican Sen. Lisa Murkowski broke from the GOP on Obamacare repeal this week, the Alaska Dispatch News reported.

Zinke, who heads the agency that oversees federal land and natural resources, spoke to Murkowski and GOP Sen. Dan Sullivan, who represent a state that relies heavily on energy. Sullivan told the Dispatch News that he feared "the strong economic growth, pro-energy, pro-mining, pro-jobs and personnel from Alaska who are part of those policies are going to stop."

The calls came after Trump tweeted Wednesday morning that Murkowski "let the Republicans, and our country, down" by casting one of two GOP votes against a motion to start debate on some form of Obamacare repeal. Senate Republicans are pushing to pass an Obamacare repeal plan this week despite party divisions and concerns from Murkowski and others that current repeal or replacement options will not adequately fix Obamacare's flaws.

Murkowski could prove decisive this week as the GOP seeks to approve a so-called skinny Obamacare repeal in what will likely be a tight vote. Murkowski has shrugged off Trump's criticism and told reporters Thursday that she would characterize the call from Zinke more as a difficult conversation than a threat.

"I'm a pretty strong and independent individual," she said. "I listen to the input from all sides, whether it is the president, whether it is certainly the secretary of Interior where we have much, much in common, and always absolutely, the people of Alaska."

Murkowski said that she and Zinke talked about energy issues as well as health care.

A spokesperson for Sullivan, as well as the White House and Interior Department, did not immediately respond to CNBC's requests for comment.

Read the full Alaska Dispatch News report here.