After weeks of rising tensions with President Trump, President Vladimir V. Putin of Russia picked up the phone.

The Kremlin said Russia had initiated the call on Thursday between the two leaders, a telling acknowledgment of a Russian priority as important as any battlefield in Ukraine: appeasing Mr. Trump.

Even as Mr. Putin has pounded Ukrainian cities and waged grinding warfare in the country’s east, he has invested dozens of hours into flattering Mr. Trump, dangling the prospect of Russian-American business deals and sending the message that Russia is open to talks to end its invasion.

The tactic has helped Mr. Putin head off repeated deadlines and sanction threats by the American president without curtailing Russia’s war effort.

In June, a time when some Republican allies of Mr. Trump were pushing for sanctions against Russia, Mr. Putin called Mr. Trump to wish him a happy birthday; Mr. Trump said Mr. Putin had acted “very nicely,” and the sanctions never appeared.

In August, as Mr. Trump was threatening to enforce a 12-day deadline for Mr. Putin to end the war, the Russian leader hosted Steve Witkoff, the White House envoy and close friend of Mr. Trump, for a three-hour meeting that set the stage for the two presidents’ summit in Alaska.

This week, the cease-fire in Gaza gave Mr. Putin a new pretext to call — and praise — Mr. Trump. More relevant to Mr. Putin, however, was the fact that President Volodymyr Zelensky of Ukraine was scheduled to visit the White House on Friday. ——New York Times