By Amanda Becker and Robert Iafolla

WASHINGTON (Reuters) - President-elect Donald Trump named fast-food executive Andy Puzder to head the U.S. Department of Labor on Thursday, drawing criticism from labor advocates worried about his opposition to a higher minimum wage and government regulation of the workplace.

Puzder, chief executive of CKE Restaurants Inc [APOLOT.UL], which operates the Carl's Jr. and Hardee's fast-food chains, has frequently argued in the media that higher minimum wages would hurt workers by forcing restaurants to close.

He has bashed a new Labor Department rule aimed at extending overtime pay to more than 4 million U.S. workers and has praised the benefits of automation in the fast-food industry.

Fast-food workers, who are largely not unionized, are engaged in a multi-year campaign known as the "Fight for $15," which is supported by labor unions, to raise minimum wages to $15 per hour. They have had state-wide successes in New York and California and in cities and municipalities such as Seattle.

Trump, in a statement released by his transition team, praised Puzder for a "record fighting for workers" and said he would ensure occupational safety standards.

"He will save small businesses from the crushing burdens of unnecessary regulations that are stunting job growth and suppressing wages,” Trump said.

In the same statement, Puzder said he agreed with Trump that "the right government policies can result in more jobs and better wages for the American worker."

The Labor Department regulates wages, safety and discrimination in the workplace.

Republican Trump beat Democrat Hillary Clinton in last month's election by carrying swing states - and some traditionally Democratic states - in the U.S. Rust Belt after promising to create jobs and to review or cancel trade deals that he said were bad for workers.

National labor leaders had urged their rank-and-file members to back Clinton, saying Trump's appointments and policies would not align with his promises to workers.

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Labor leaders have been girding for Trump to appoint pro-business regulators at the Labor Department and National Labor Relations Board, and to roll back key regulatory initiatives of the Obama administration such as the Labor Department rule granting overtime pay to more than 4 million salaried workers, both unionized and not unionized.

"He was talking a good game when he was running for president, as far as helping workers and leveling the playing field for them, but with the nominations he's made it's just the opposite," said Lee Saunders, president of the public employees union AFSCME.

Although just 11.1 percent of U.S. workers were represented by a union in 2015 - down from 20.1 percent in 1983, the first year government statistics were kept - labor unions are a powerful force in Democratic politics. But union members' support for Clinton at the election was lower than it had been for President Barack Obama four years ago.

About 51 percent of voters from union households backed Clinton, with 42 percent supporting Trump, a CNN exit poll showed. Obama won 58 percent of the same voters in his 2012 re-election win against Republican Mitt Romney.

Business groups welcomed the appointment of Puzder. Robert Cresanti, president of the International Franchise Association, an industry group, praised him as an "exceptional choice" who would bring "business experience and policy acumen on so many issues impacting employers and employees."

But Democrats were critical.

"In Andrew Puzder, Trump found a Labor Secretary that would help him roll back the minimum wage, end the overtime rule that will raise wages for millions, weaken safeguards for workers, and to wipe out unions," said American Bridge, a liberal advocacy group.

DISPUTE WITH UNION LEADER

Trump's decision to pick Puzder comes as he is engaged in a Twitter dispute with the head of a local United Steelworkers union in Indiana.

United Steelworkers Local 1999 President Chuck Jones, who represents workers at United Technologies Corp's Carrier plant in Indianapolis, criticized Trump for inflating the number of jobs that would be saved by his intervention in the company's decision to move some production to Mexico.

Trump responded on Twitter that Jones has done a "terrible job representing workers."

Jones said after speaking to the company that 800 jobs will remain in Indianapolis and 730 of those will be union jobs, with another 70 management positions. But Trump said last week that a deal made by Indiana to give the company $7 million in tax breaks would keep 1,100 jobs in the region.

"Our people, at that point in time, got their hopes back up that they might have a job," Jones told CNBC on Thursday. "I’ve said at every interview that I’m grateful for President-elect Trump getting involved … without his involvement these 800 jobs would not remain in Indianapolis."

"All he had to do is come back and say I was misled by (United Technologies) ... instead of doing that he goes on the attack on me?" Jones added. Jones has said some of the president-elect's supporters sent him death threats.

(Additional reporting by Julia Edwards Ainsley, David Shepardson and Emily Stephenson; Editing by Alistair Bell and Frances Kerry)