By Lisa Lambert

WASHINGTON (Reuters) - U.S. Democrats' liberal firebrand, Senator Elizabeth Warren, threw down the gauntlet to President-elect Donald Trump on Thursday, telling labor union members there are financial and social issues where her party will fight him and continuing to blast the Republican.

Battling bigotry is the first job for Democrats after the election, said Warren, of Massachusetts, giving a sense of how her party will operate now that it no longer controls the White House and remains the minority in both chambers of Congress.

"We will fight back against attacks on Latinos, African Americans, women, Muslims, immigrants, disabled Americans - on anyone," said Warren, who sparred frequently over Twitter with Trump and criticized him on the campaign trail in the weeks leading up to Tuesday's election. "Whether Donald Trump sits in a glass tower or sits in the White House, we will not give an inch on this, not now, not ever."

She said Trump had "encouraged a toxic stew of hatred and fear" and during the campaign "regularly made statements that undermined core values of our democracy."

In the speech to the AFL-CIO labor federation, Warren also said Democrats will resist attempts to loosen financial regulation, "gut" the Dodd-Frank Wall Street reform law and eliminate the Consumer Financial Protection Bureau (CFPB).

"If Trump and the Republican Party try to turn loose the big banks and financial institutions so they can once again gamble with our economy and bring it all crashing down, then we will fight them every step of the way," she said.

Warren did highlight areas of agreement. She said "count me in" on Trump's support of a new Glass-Steagall law to separate investment and retail banking, reforming trade deals, maintaining Social Security benefits, helping on childcare and college costs and rebuilding infrastructure.

Warren rose to lead the liberal wing of the party during the 2007-2009 financial crisis. After Republicans blocked President Barack Obama's attempt to appoint her as the first director of the CFPB, she won a seat in Congress.

In 2015, progressive groups and a political action committee pressed her to run for president. Since Trump's victory on Tuesday, many have already renewed their calls, for the 2020 presidential election.

(Reporting by Lisa Lambert; Editing by Meredith Mazzilli)