The expected announcement, which Mr. Biden had signaled when he was a candidate last year, has been welcomed by Armenians and human rights advocates. It carries enormous symbolic weight, equating the anti-Armenian violence with atrocities on the scale of those committed in Nazi-occupied Europe, Cambodia and Rwanda. Use of the term is a moral slap at President Tayyip Recep Erdogan of Turkey, a fervent denier of the genocide. He has fulminated at other leaders, including Pope Francis, for describing the Armenian killings that way... As vice president in the Obama administration, Mr. Biden never enjoyed an easy relationship with Mr. Erdogan, an autocratic leader who gave him an icy reception in August 2016. The two met a month after the failed coup in Turkey that Mr. Erdogan blamed on a Turkish cleric living in exile in the United States. Perhaps more important, Mr. Erdogan’s closeness to President Vladimir V. Putin of Russia, Turkey’s testy relations with other NATO allies and its purchase of Russian antiaircraft missiles have irritated the Biden administration and both houses of Congress. And Turkey’s increasing economic problems under Mr. Erdogan may have made him less likely to retaliate against any American declaration that offends him.