BONN, Germany — By the time Secretary of State Rex W. Tillerson decided that he wanted to join his counterparts at an important global gathering in Bonn — his first trip overseas as America’s top diplomat — all the good hotel rooms in this small German city had been taken.

So Mr. Tillerson and his entourage of temporary State Department helpers took rooms at a rambling health clinic and spa next to a public bathhouse in the picturesque town of Bad Neuenahr, more than 20 miles outside the city — a bit like holing up in Beltsville, Md., for a conference in Washington.

The remoteness of the location fit with the growing distance between the Trump administration and its European counterparts on such issues as immigration, refugees, defense and trade. Indeed, so much uncertainty has crept into what had been close relations that Mr. Tillerson largely dispensed with the usual gushing and grinning news conferences with his counterparts on Thursday at the gathering of foreign ministers from countries in the Group of 20. The meeting was called to lay the groundwork for the summit meeting of leaders of G-20 countries in Hamburg in July.

With the Russians, though, Mr. Tillerson repeated what has become an increasingly hard line in the administration against the kind of warming ties that President Trump presaged in his campaign. In brief remarks after meeting the Russian foreign minister, Sergey V. Lavrov, Mr. Tillerson said that Russia needed to honor its commitments to “de-escalate the violence in Ukraine.”