WASHINGTON - The House voted overwhelmingly on Tuesday to formally recognize the Armenian genocide and denounce it as a matter of American foreign policy, a symbolic vindication for the Armenian diaspora made possible by a new torrent of bipartisan furor at Turkey. The passage of the legislation, by a 405-to-11 vote, is the first time a chamber of Congress has officially designated the 1915 mass killings of an estimated 1.5 million Armenians at the hands of the Ottoman Empire as a genocide. Lawmakers had previously shirked from supporting such a resolution to preserve the United States’ relationship with Turkey, a NATO ally that has steadfastly denied that the atrocities amounted to genocide. Livid at Turkey’s bloody military assault in northern Syria, some lawmakers saw an uneasy parallel between the Armenian genocide and the bitter warnings from Kurdish forces that the withdrawal of American forces would lead to the ethnic cleansing of their people. “Recent attacks by the Turkish military against the Kurdish people are a stark reminder of the danger in our own time,” Speaker Nancy Pelosi of California said in a speech on Tuesday. And so Ms. Pelosi moved to put the measure, led by Representative Adam B. Schiff of California, the chairman of the Intelligence Committee, to a vote for the first time. “Too often, tragically, the truth of the staggering crime has been denied,” she said. “Today, let us clearly state the facts on the floor of this House to be etched forever into the Congressional Record: The barbarism committed against the Armenian people was a genocide.” The House vote was bound to infuriate leaders in Turkey. Almost immediately after the vote, Turkey’s foreign minister, Mevlut Cavusoglu, assailed it on Twitter as an act of revenge by American lawmakers unhappy over Turkey’s military moves against the Kurds. “This shameful decision of those exploiting history in politics is null & void for our Government & people,” he wrote.