Russian President Vladimir Putin gestures during a news conference in Moscow. (Pavel Golovkin/Associated Press)

COULD IT have been just a coincidence that Russian-backed forces in Ukraine launched their biggest offensive in months the day after Vladi­mir Putin spoke by phone with President Trump? Somehow, we doubt it. Rather, the volleys of Grad rockets and heavy artillery that have been raining down on Ukrainian army positions since Sunday look a lot like a test of whether the new president will yield to pressure from Moscow.

Mr. Trump and Mr. Putin didn’t speak much about Ukraine during their call; officials told us that Mr. Trump called it “a tough issue” before moving on. Nor did the White House issue a widely rumored executive order abruptly lifting U.S. sanctions on Moscow for its invasions of Crimea and eastern Ukraine. That may have been due to pushback Mr. Trump heard from British Prime Minister Theresa May on Friday, as well as from senior congressional Republicans.

Perhaps a disappointed Mr. Putin felt the need to do some pushing from the other side. Or maybe he wanted to wreck a meeting Ukrainian President Petro Poroshenko had scheduled for Monday with German Chancellor Angela Merkel, his strongest Western supporter. In any case, Russian guns that had been quiescent for weeks suddenly erupted Sunday near the government-controlled town of Avdiivka, north of the separatist-held city of Donetsk. The shelling soon spread south to Mariupol, a key government-held city on the coast of the Sea of Azov. One sign the offensive was serious and Kremlin-directed: Ukrainian soldiers and civilians were swamped with threatening text messages characteristic of Russian electronic warfare units.

Russia, predictably, blamed Ukraine for the fresh fighting, and Ukrainian commanders acknowledge that in recent weeks their forces had moved some positions forward in the no-man’s land between the front lines. But Mr. Poroshenko, who was forced to break off his trip to Germany, has scant cause to seek another round of warfare in the east when the past two have led to crushing Ukrainian defeats. In Kiev, the Ukrainian economy is showing signs of revival; positive growth was reported for 2016, while Russia remained in recession. Slow progress is being made on economic and institutional reforms. The new fighting places those at risk.

That’s likely one of Mr. Putin’s aims. Another is to speed Mr. Trump toward the concessions Moscow seeks: not just the lifting of sanctions, but also the acceptance of a Russian sphere of influence including Ukraine. In exchange for what? Mr. Putin offers “cooperation” in fighting the Islamic State in the Middle East, a possibility repeatedly touted by Mr. Trump. But that U.S.-Russian military cooperation has also been a prime objective of Mr. Putin’s. In other words, the deal he’s offering is something he really wants in “exchange” for something else he really wants.

If Mr. Trump goes along with this, Mr. Putin will achieve a third objective — diminishing U.S. global influence to the gain of Russia. That’s what congressional leaders such as Sen. John McCain (R-Ariz.) have been trying to point out to Mr. Trump, and what the past two presidents’ history with Mr. Putin vividly demonstrates. If the White House chooses to ignore all that, Ukraine will not be the only loser.