When President Biden declared to reporters on Wednesday, almost off the cuff, that President Vladimir V. Putin was a “war criminal,” he was speaking from the heart, his aides said, reacting to the wrenching images of civilians — including children — being dragged, dead or disfigured, from ruins of buildings shelled by Russian forces.

But he was also personalizing the conflict, in a way past presidents have avoided at moments of crisis with the United States’ leading nuclear-armed adversary. And his remark underscored how personal condemnation has become policy, as Mr. Biden and his top aides frame Mr. Putin as a pariah, an indiscriminate killer who should be standing trial at The Hague…

But what began as a visceral reaction appears to reflect a strategic decision. Branding Mr. Putin as a war criminal supports the administration’s case as it simultaneously tries to keep the Western alliance unified and attempts to pressure China not to bail Mr. Putin out of his economic crisis and military mistakes. That effort will face a new test on Friday when Mr. Biden is scheduled to talk to President Xi Jinping of China for the first time since the invasion, and warn him against supplying weapons to Mr. Putin.