By Steve Holland and Jeff Mason

CANFIELD, OHIO/CLEVELAND (Reuters) - Donald Trump and Hillary Clinton took their bitter fight for the White House to the battleground state of Ohio on Labor Day on Monday, mingling with voters at a fair, a parade and a brewery as the race entered its final, frenzied two months.

Trump, more accustomed to presiding over big rallies from a stage, plunged into a crowd at a county fair where supporters had built a replica of the wall the Republican nominee has pledged to build along the U.S.-Mexico border.

"This has been an unbelievable reception!" Trump said at the Mahoning County Fair after exiting his SUV to shake hands with the crowd. Earlier in the day, he met with leaders and members of various unions in a Cleveland suburb to discuss immigration and trade, his two signature issues.

Democratic nominee Clinton stopped at a brewery in Cleveland before heading to a nearby Labor Day parade and rally, where she tested a new jab at her opponent: "Friends don't let friends vote for Trump."

At one point, in a sign of the state's importance, Clinton's and Trump's planes sat side-by-side on the tarmac in Cleveland, though the nominees did not cross paths.

"It's kind of interesting to have all the planes here on the same tarmac. It just shows you how important Ohio is,” said Clinton's running-mate, U.S. Senator Tim Kaine of Virginia, who was campaigning alongside her.

The Labor Day holiday traditionally kicks off the last stretch of campaigning ahead of the Nov. 8 election. While most polls show Trump trailing Clinton in many battleground states where the election will likely be decided - including in Ohio - he has drawn close to even with her in some national polls and even inched ahead in others.

The most recent Reuters/Ipsos poll on Friday showed Trump had the support of 40 percent of likely voters to 39 percent for Clinton, erasing her recent eight-point lead.

Both candidates also coincided in making overtures to the news media covering them.

Clinton, traveling with her press corps for the first time on a new plane emblazoned with her campaign slogan, "Stronger together," said on Monday she had enjoyed the “last moment before the mad dash” to the finish line and that she was “more than ready” for the next nine weeks.

Her Republican rival, also campaigning with his vice presidential pick, Indiana Governor Mike Pence, invited his press corps for the first time to accompany him on the short flight from Cleveland to Youngstown.

En route, Trump told reporters on the plane that he was open to the idea of them traveling with him more often and that there is an "obligation" for nominees to participate in the three upcoming presidential debates.

TRUMP’S REBOUND

Trump’s rebound from a series of self-inflicted wounds has followed the hiring of a new campaign management team, and the Republican nominee is showing more discipline on the stump, reading his rally speeches from teleprompters.

Trump has been helped by what his campaign said was a positive week last week in which he made a quick trip to Mexico, appearing side by side with Mexican President Enrique Pena Nieto, and visited a black church in Detroit.

An immigration speech Trump gave following his trip to Mexico, however, drew criticism from some of his Hispanic supporters, and several backers advising him on the issue decided to part ways with his campaign.

Trump aide Jason Miller said rising poll numbers showed that the Republican nominee's campaign was moving in the right direction.

“The trend lines are the important thing to point to," Miller told Reuters. "The problem that Clinton has is there is no positive information flow for her campaign."

Clinton, who was President Barack Obama's first-term secretary of state, appeared at few public campaign events during the latter half of August, instead raising funds at high-dollar events in the East Coast vacation spots of Martha’s Vineyard and the Hamptons, and with celebrities in Los Angeles and high-tech leaders in Silicon Valley.

Clinton’s campaign announced that it had raised $143 million in August for her presidential bid and the Democratic Party.

Clinton is again on the defensive over her use of a private email server and possible conflicts of interest with her family foundation while secretary of state, which have caused unease for some voters. But experts still see the Democratic nominee as the odds-on favorite to win the presidency.

(Reporting by Jeff Mason and Steve Holland in Ohio; Additional reporting and writing by Amanda Becker in Washington; Editing by Jonathan Oatis)