U.S. Sen. Lisa Murkowski of Alaska is one Republican who hasn’t always seen eye to eye with President Donald Trump.

But in a recent conversation with a newspaper’s editorial board, Murkowski said she and Trump had a surprising first phone conversation when Trump was still president-elect – and she used the opportunity to try to build a connection.

Murkowski told the Anchorage Daily News that she reached out to Trump’s office to offer a suggestion for who Trump should pick for secretary of the interior. (The job ultimately went to Ryan Zinke of Montana.)

“It was a Saturday morning, and I call this number, and this man answers. I'm like, ‘Hello, this is Lisa Murkowski, I'd like to leave a message for Mr. Trump,’” Murkowski told the newspaper.

“So he says, ‘How are you?’ And then he goes on to say, ‘You know, I really love Alaska, I'm just fascinated by Alaska.’ And I said, ‘And to whom am I speaking?’ And he said, ‘Well, this is Donald Trump!’"

Murkowski said she immediately saw an opportunity to “come clean with this guy” whom she hadn’t supported for president.

“And I said, ‘But here's the deal: You won; I won. You want to do good things for the country; I want to do good things for the state. I figure we can be working together to do just that.’ And he said, ‘Absolutely,’” Murkowski recalled.

"You won; I won. You want to do good things for the country; I want to do good things for the state." — U.S. Sen. Lisa Murkowski, R-Alaska, recalling a phone conversation with President-elect Donald Trump

“And that's kind of how we have approached the issues that we've been working on,” she said.

But the Trump-Murkowski relationship has faced several tests since then.

In July 2017, for example, Murkowski and U.S. Sen. Susan Collins of Maine were the only Republicans to oppose a procedural motion to begin a debate on rolling back ObamaCare.

Trump expressed his disappointment, in a tweet.

“Senator @lisamurkowski of the Great State of Alaska really let the Republicans, and our country, down yesterday. Too bad!” the president tweeted.

Then in December 2017, Trump invited Murkowski and other Republicans to a luncheon to discuss a still-pending tax bill, but the Alaskan was a no-show, Anchorage's KTUU-TV reported.

She ultimately backed the bill, for which she authored an energy provision that opened up the Arctic region to oil drilling.

Then just this week, Murkowski told E&E News that she wasn’t totally behind Trump’s “national security” rationale for propping up the nation’s struggling coal and nuclear plants.

“Competition has gotten us to a pretty good place with our markets, quite honestly,” she told the outlet. “And now we're basically going to be directing a few, specific industries from within. I'm just not convinced that's the right way to go.”

Nevertheless, the data site FiveThirtyEight.com in May showed Murkowski to be in agreement with Trump’s positions more than 83 percent of the time.