AVDIIVKA, Ukraine — Here at the epicenter of the latest spasm of violence in eastern Ukraine, great thuds of artillery shells could be heard in the distance on Friday, as residents scrambled to board up blown-out windows and stockpile groceries in anticipation of further shelling.

Dozens of soldiers and civilians have been killed or wounded all along the front in nearly two weeks of fighting. While it is still not clear who is responsible for the escalation in fighting between the Ukrainian Army and the Russian-backed rebels, many residents say they believe the recent violence was meant to force some clarity from President Trump.

So far, Mr. Trump’s administration has offered mixed messages about the three-year-old war. He has said he would be open to lifting sanctions against Russia imposed in 2014 after it annexed the Crimean peninsula and sent troops to aid separatists in the east. However, Nikki R. Haley, Mr. Trump’s newly appointed ambassador to the United Nations, last week called for an end to “the Russian occupation of Crimea” and for a halt in the fighting in eastern Ukraine.

This week, in a letter to Lithuania’s president, Mr. Trump seemed to echo that sentiment and personally expressed support for keeping Ukraine intact. The lack of a clear position on the conflict has bewildered officials on both sides, particularly in Ukraine where Mr. Trump’s overtures to President Vladimir V. Putin of Russia are viewed with alarm.