Hillary Clinton claimed the Democratic presidential nomination on Tuesday night after decisive victories in the California, New Jersey and New Mexico primaries, and she quickly appealed to supporters of Senator Bernie Sanders of Vermont to unite with her against Donald J. Trump.

The Associated Press reported early Wednesday that Mrs. Clinton had won California, but Mr. Sanders gave no indication that he would yield, insisting earlier that he would continue his campaign and barely acknowledging her achievement.

With the 14-month Democratic race nearing a close, Mrs. Clinton savored the biggest night of her extraordinary journey from lawyer, wife and first lady to senator, secretary of state and, now, the first woman to win a major party’s nomination. At a rally in Brooklyn, she took the stage with her hands clasped over her heart in gratitude, then threw open her arms in joy and savored a long moment as a jubilant crowd waved American flags and chanted “Hillary.”

Reaching for history, Mrs. Clinton pledged to build on the achievements of pioneers like the 19th-century leaders at Seneca Falls, N.Y., who began the fight for women’s rights in America.