During the presidential campaign Trump sent spasms of anxiety through America's NATO partners, blasting the transatlantic military alliance as "obsolete," and suggesting the U.S. would not come to the aid of allies who were attacked unless they boosted financial contributions.
Experts say that comments like these, combined with Trump's oft-expressed admiration for Putin, have left NATO members fearful that the alliance's strongest member would not defend them in the event of Russian aggression.
"It's not a five-alarm fire yet, because that's been talk and what comes now is actual concrete policy," said Adam Quinn, an expert in international politics at the U.K.'s University of Birmingham. "The Europeans will be keen to see … if they can steer the administration toward something more like what they would see as a workable solution."
Trump's vocal support for Britain quitting the European Union, known as Brexit, has also ruffled feathers in Europe.
At a recent summit of European leaders in Malta, presidents and prime ministers, including France's Francois Hollande, lined up to denounce Trump's comments on relations with Europe, branding the president's positions as "extremism."
Tillerson has already begun the process of trying to smooth out the relationship with EU, meeting with the bloc's foreign policy chief, Federica Mogherini, in Washington, D.C., earlier this month.