By Bernie Woodall

(Reuters) - United Auto Workers President Dennis Williams said on Tuesday that Democratic presidential nominee Hillary Clinton has assured him she would renegotiate the North American Free Trade Agreement if she is elected president.

Williams' comments come as Clinton is under pressure on international trade deals from Republican presidential nominee Donald Trump and supporters of her former Democratic rival Bernie Sanders.

Clinton has previously said she wanted to rework NAFTA. Her campaign on Tuesday declined to comment on the meeting with Williams.

Williams said he met with Clinton one-on-one prior to the union's endorsement of her in May, when Sanders was still in the race to be the Democratic party's nominee. The UAW has more than 400,000 members.

“She’s committed to me that not only would (she) dig into NAFTA but she made every indication that she would sit down and try to redo NAFTA,” Williams told reporters during a telephone press conference from Philadelphia, where he is attending the Democratic National Convention.

Williams said Clinton "recognizes that NAFTA was not the success that it was supposed to be," when her husband, Bill Clinton, pushed for it as president two decades ago.

Stephen Miller, senior policy adviser to the Trump campaign, said Hillary Clinton "will never renegotiate Bill Clinton's NAFTA."

The Trump campaign adviser said, "You can be certain when she was personally getting paid millions and millions by Wall Street and big banks to deliver secret speeches she wasn't breathing a word against globalist trade pacts."

NAFTA, which eliminated most tariffs on trade between the United States, Mexico and Canada, was promoted as a way to support economic growth by eliminating barriers to trade. Opponents say it has robbed Americans of jobs because it makes it easy for U.S. companies to move operations to Mexico where wages are much lower.

Williams said he hopes that an updated treaty would help foster stronger worker unions in Mexico, where many auto manufacturers have factories.

"She told us all that," AFL-CIO President Richard Trumka said in an interview, referring to Clinton's assurances to labor unions that she would rework NAFTA.

The AFL-CIO, a federation of unions which includes the UAW, stayed neutral during the Democratic primary but endorsed Clinton in June once it was clear she would become the party's nominee. The UAW endorsed Clinton in May.

Williams said that support among UAW members for a Trump presidency has fallen to about 19 percent from 28 percent last year, before Trump said that new automotive industry jobs could be placed in states without strong union support at lower wages than those earned by UAW members.

(Additional reporting by Amanda Becker in Philadelphia; Editing by Phil Berlowitz, Leslie Adler and Bernard Orr)