Clinton Declares Herself U.S. Democratic Presidential Nominee

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WATCH: Clinton Claims Victory, Takes Aim At Trump, As Sanders Fights On (AP video)

Hillary Clinton has claimed victory in her battle for the Democratic presidential nomination, with President Barack Obama congratulating her.

The former first lady, U.S. senator, and secretary of state celebrated her victory over rival Bernie Sanders in a grueling primary election race amid cheering supporters in Brooklyn, New York, late on June 7. She said her feat crowns a long history of women's achievements at gaining rights.

"Thanks to you, we have reached a milestone," Clinton said. "First time in our nation's history that a woman will be a major party's nominee... We all owe so much to who came before."

"Tonight, we can say with pride that, in America, there is no barrier too great and no ceiling too high to break."

The White House said Obama called Clinton to congratulate her on securing "the delegates necessary to clinch" the Democratic nomination. Obama also called Sanders, who has not conceded the race, and will meet with him on June 9.

Clinton, 68, won the June 7 Democratic primary contests in California, New Jersey, New Mexico, and South Dakota, expanding her lead in the number of delegates needed to clinch the nomination and setting up a five-month campaign against presumptive Republican nominee Donald Trump that will end with the presidential election on November 8.

Sanders, who won the Democratic caucuses in North Dakota and Montana, vowed to continue his quest for the White House, telling supporters in California that he will fight on to compete in next week's primary in Washington, D.C.

The Vermont senator said that, after that election, "we take our fight for social, economic, racial, and environmental justice to Philadelphia," where the Democratic National Convention will take place next month.

Trump -- who had already secured enough delegates to ensure his nomination at the Republican convention next month -- won in the largest state, California, as well as in Montana, New Mexico, South Dakota, and New Jersey.

With reporting by Reuters, dpa, and AP