Hours after Hillary Clinton claimed the Democratic presidential nomination, Bernie Sanders insisted he's not leaving the race quite yet.

"The struggle continues," the Vermont senator said.

Speaking Tuesday evening in Santa Monica, California, Sanders acknowledged the difficulty of the fight ahead -- Clinton has won a majority of pledged delegates, so Sanders would have to persuade many unpledged delegates, or superdelegates, to change their votes in order for him to win.

"I am pretty good at arithmetic, and I know that the fight in front of us is a very, very steep fight," he said.

However, he said he stood by his promise to remain in the contest until the Democratic National Convention in July, vowing to "fight on."

"We are going to fight hard to win the primary in Washington, D.C., and then we take our fight for social, economic, racial and environmental justice to Philadelphia," he said.

Sanders railed against presumptive GOP nominee Donald Trump, who has come under fire from his own party for a series of racist remarks in recent days.

"The American people will never support a candidate whose major theme is bigotry, who insults Mexicans, who insults Muslims and women and African-Americans," Sanders said.

Sanders has trailed Clinton in delegates throughout the primary. On Monday evening, The Associated Press declared Clinton the presumptive nominee, angering Sanders' campaign and supporters.

"It is unfortunate that the media, in a rush to judgement, are ignoring the Democratic National Committee’s clear statement that it is wrong to count the votes of superdelegates before they actually vote at the convention this summer," spokesman Michael Briggs said in a statement Monday.

Sanders is set to meet with President Barack Obama on Thursday to discuss the state of the campaign.