By Ginger Gibson

WASHINGTON (Reuters) - Republican presidential nominee Donald Trump's promise to restore American jobs by renegotiating international trade deals appears to be failing him in states most affected by outsourcing, according to a Reuters/Ipsos poll.

Voters in Michigan, Ohio and Pennsylvania - three competitive states in the Nov. 8 election that form the bulk of a region dubbed the Rust Belt for its swaths of shuttered factories - favor Trump's Democratic rival, Hillary Clinton, on the issue of trade, according to the polling, with some respondents citing how international trade can bring down prices.

The results underscore the uphill battle the New York businessman faces on Election Day, when he needs to sweep a broad array of battleground states to win the White House.

"Trump has made a strong effort to portray Clinton as favorable to trade policies that he has labeled 'a disaster' for the United States," said Thomas Nelson, a political science professor at Ohio State University.

In the automaking state of Michigan, which has voted reliably for Democratic candidates in recent presidential elections but which Trump has fought hard to win, some 40 percent of likely voters believed Clinton would be better equipped to address trade, compared with 36 percent for Trump.

In Ohio, known for its aerospace, steel and rubber industries, 45 percent said Clinton would be better on trade, compared with 38 percent for Trump. In Pennsylvania, long a steel and heavy manufacturing center, 45 percent favored Clinton on trade, compared with 38 percent for Trump, according to the polling, conducted in mid-October.

Clinton is leading Trump in all three states among likely voters, with advantages of 4 points in Michigan, 3 points in Ohio and 6 points in Pennsylvania, according to the Reuters/Ipsos polling.

But other polls show the race tightening in those states. RealClearPolitics, which averages data from most major polls, shows Clinton leading Trump by 6.6 points in Michigan and 5.1 points in Pennsylvania, and Trump leading Clinton by 2.7 points in Ohio.

Officials for Trump's campaign did not respond to a request for comment.

'WHAT JOBS ARE YOU BRINGING BACK?'

Poll respondents reached by Reuters who favored Clinton on trade mainly gave two reasons - first, that international trade deals can help people by lowering prices for goods; and second, they doubt Trump can deliver on his promise to restore the U.S. manufacturing sector.

“We all like to have inexpensive items," Ronald Lane, 56, of Canonsburg, Pennsylvania, who plans to vote for a third-party candidate next week as a protest against both Trump and Clinton.

"I think it’s important to save American jobs which have already gone overseas, but I don’t believe there is much that can be done to bring them back," he said.

Christina Ledesma, of Grand Rapids, Michigan, a Clinton supporter, said she also disagreed with Trump that the economy would suffer a lasting negative effect from trade deals.

"Our unemployment rate is lower than it’s been since 2008. What jobs are you bringing back?" she said.

Michigan's unemployment rate was 4.6 percent in September, below the national average of 5 percent. Ohio's was at 4.8 percent and Pennsylvania's at 5.7 percent.

Trump has called the North American Free Trade Agreement with Canada and Mexico one of the worst deals ever struck and blames it for manufacturing jobs being moved to Mexico.

He also opposes the Trans-Pacific Partnership, which would open markets in East Asia. Trump argues that the deal, which must be ratified by Congress, would motivate more U.S. companies to move their production overseas.

Last week while campaigning, he called outsourcing “the greatest job theft in the history of the world".

"The jobs theft will end … the day I start the presidency. It’s going to be America first again," he said.

Clinton has offered a more tempered approach, saying she would seek to re-evaluate NAFTA if elected and that there were problems with some aspects of the TPP.

The Reuters/Ipsos poll was conducted online in English from Oct. 6 to Oct. 17 in Michigan and Pennsylvania, and from Oct. 6 to Oct. 12 in Ohio. It included 1,370 likely voters in Michigan, 1,467 in Pennsylvania, and 1,200 in Ohio. All three state polls had a credibility interval, a measure of accuracy, of 3 percentage points.

(Reporting by Ginger Gibson; Additional reporting by Alana Wise and Chris Kahn; Editing by Richard Valdmanis and Peter Cooney)