By Steve Holland and Jeff Mason

CANFIELD, Ohio/CLEVELAND (Reuters) - Donald Trump and Hillary Clinton opened a final two-month sprint to the Nov. 8 election on Monday with the Republican presidential nominee suddenly looking stronger as he and his Democratic rival took their bitter fight to Ohio.

Both Trump and Clinton made overtures to a news media that each candidate sees as often hostile to them, talking to reporters on their private planes. Clinton's session with reporters was her first news conference since last December.

After eating a gyro at a diner in the Cleveland area, Trump rallied thousands of cheering supporters at a county fair in Canfield, and Clinton visited a brewery in Cleveland. For a time, their planes were parked about 200 yards apart at the Cleveland airport, a sign of Ohio's importance in the election.

Ohio is considered one of four swing states - those that are not clearly in the Democratic or Republican camp - that could prove decisive in the Electoral College vote that will ultimately determine the winner. The other swing states are Florida, Pennsylvania and Virginia.

Trump was buoyed by more polls showing him in a competitive position. The latest Reuters-Ipsos poll showed Trump with 40 percent support vs 39 percent for Clinton, effectively ending Clinton's bump up in the polls after the Democratic nominating convention. Other polls showed Clinton's lead had shrunk.

"I think we've had a great month," Trump said.

Clinton remained in a strong position to win the White House race, but Trump and his team cited his growing strength in opinion polls nationally and in several states where the election is likely to be decided to argue that his message is breaking through to voters.

Clinton, who emerged into the public eye after days of raising money from wealthy donors behind closed doors, said she always knew the race would be close.

"We’re just going as hard and fast as we possibly can to be organized for turning out the vote, because we’ve always thought this was going to be hard, and that’s why, you know, I’m not worried, I’m just working," she said.

Trump, shaking his fist triumphantly, plunged into a crowd at the Mahoning County Fair where supporters had built a replica of the wall that the Republican nominee has pledged to build along the U.S.-Mexico border.

"This has been an unbelievable reception!" Trump said after maneuvering through a crowd of people who shouted his name, against a backdrop of food stands offering fare ranging from chicken on a stick to Italian sausages, fudge and fresh corn.

Inviting reporters onto his plane for the first time since accepting the Republican presidential nomination, Trump said his focus going forward will be on how to create jobs for middle-class Americans.

He has spent most of the past two weeks trying to clarify his position on illegal immigration, first flirting with a softening, then reinforcing his hardline approach, and then, on his plane, saying undocumented people might ultimately get on a path to a legal status once border enforcement steps are taken.

"I'm all about the jobs now," he said, saying his position on the immigration issue was now well known.

He also pledged to participate in all three televised presidential debates, ending speculation that he might sit out one or more if he was not happy with the format. His first face-off with Clinton is at Hofstra University in New York state on Sept. 26.

Clinton made her stop 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."

The Labor Day holiday traditionally kicks off the last stretch of campaigning ahead of the November election.

Speaking to reporters on her new campaign plane, she took credit for Trump's overture to the news media. Clinton, buffeted by controversy over her use of a private email server as U.S. secretary of state, has been criticized by Republicans and the news media for months for failing to hold a news conference.

"I heard now that we’ve got this great plane, that Donald Trump actually invited his press on his plane where I’m told he even answered a few questions," said Clinton.

TRUMP’S REBOUND

Trump’s rebound from a series of self-inflicted wounds follows the hiring of a new campaign management team, and the Republican nominee is showing more discipline on the stump.

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

But an immigration speech that Trump gave following his trip to Mexico 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 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 and Leslie Adler)