The U.S. and Russia aired disagreements this week over key world conflict zones, framing differences that spell increasing uncertainties for the start of 2018 in Europe, Asia and the Middle East.

U.S. Secretary of State Rex Tillerson, in a call to Russian counterpart Sergei Lavrov, urged Russia to moderate its stance toward Ukraine, the State Department said Wednesday, while Mr. Lavrov exhorted the U.S. to back away from confrontation with North Korea.

Tensions...