By Steve Holland and Amanda Becker

GREENVILLE, N.C., Va./WASHINGTON (Reuters) - Republican presidential nominee Donald Trump invoked religion, talked of unifying Americans and tried to raise doubts about whether Democratic rival Hillary Clinton can be trusted in a new campaign stump speech unveiled on Tuesday.

"I will fight for Detroit, for Chicago, for Baltimore, and for every neglected part of this nation – and I will fight to bring us all together as one American people," Trump told a packed rally in Greenville, North Carolina, in a departure from his typical bare-knuckled approach.

On the Democratic side, both Clinton and her vice presidential running mate, Tim Kaine, blasted Trump. Clinton focused on Trump's past bankruptcies and his refusal to release his tax records.

“He clearly has something to hide. We don’t know exactly what it is, but we’re getting better guesses about what it probably is," she said in Tampa, Florida.

Kaine, in a national security speech in Wilmington, North Carolina, criticized Trump's business dealings with Russia, the ties between some of his campaign advisers to the country and Trump’s suggestion that he hoped Russian hackers could find missing emails from when Clinton was secretary of state.

“He has openly encouraged Russia to hack his political opponents and commit espionage against his own country,” Kaine said.

Trump, in a speech on Wednesday in Cleveland, is to lay out a military preparedness plan in which he will call for rescinding mandatory defense spending cuts and embarking on a major military buildup.

The Trump campaign said the candidate will call for big increases in spending for new ships, planes, submarines and training combat troops and bolstering missile defense systems. Trump will also criticize Clinton for "military adventurism" for her handling of Libya and the Middle East as secretary of state.

Trump, buoyed by polls showing him as gaining ground against Clinton, outlined what he would do on his first day as president if elected on Nov. 8, part of a new effort to inject more discipline into his free-wheeling campaign.

He said he would suspend the resettlement of Syrian refugees into the United States, start toward repealing and replacing President Barack Obama's signature healthcare plan, and begin the first steps toward building a wall along the U.S. southern border with Mexico.

Trump, who rarely mentions religion, quoted from a Bible passage he read aloud at a black church in Detroit on Saturday, part of his effort to appeal to African-American voters.

"Imagine what our country could accomplish if we started working together as one people, under one God, saluting one flag," he added. "It is time to break with the bitter failures of the past, and to embrace a new American future."


But Trump was unflinchingly critical of Clinton over the latest disclosures from the Federal Bureau of Investigation about her use of a private email server and destruction of thousands of emails that she and her staff had deemed of a personal nature.

At least two of her mobile devices were reported destroyed by a staff using a hammer and BleachBit software to wipe unwanted emails.

"People who have nothing to hide don’t smash phones with hammers. People who have nothing to hide don’t bleach their emails or destroy evidence to keep it from being publicly archived as required under federal law," Trump said.

Kaine, in his first major policy speech since being tapped as Clinton’s running mate, drew a contrast between how Trump would approach U.S. relations with Russia and Clinton’s track record as head of the U.S. State Department from 2009 to 2013, during Obama's first term as president.

As head of the State Department, Clinton oversaw “hard-nosed negotiations” with Russia to reduce nuclear stockpiles and destroy Syrian chemical weapons, while still going “toe-to-toe” with Putin to protect America and NATO allies, Kaine said. “Trump seems to support Russian interests at the expense of American ones,” he added.

Kaine’s speech began less than an hour after Trump concluded a campaign stop in Virginia Beach, in Kaine's home state of Virginia, where he scoffed at the idea that Clinton would hold any sway over Putin’s actions.

“Putin looks at Hillary Clinton and he laughs. Putin looks at Hillary Clinton and he smiles,” Trump said.

The back-and-forth occurred as the focus of the U.S. battle for the White House shifted to national security, with both Clinton and Trump set to participate in a televised forum on Wednesday hosted by a veteran’s group.

Trump followed up his Virginia event by meeting with the wives of U.S. military personnel stationed at nearby installations. Setting aside his usual bombast, Trump turned soft-spoken and nodded attentively as the women, some of whom held babies on their laps, described their concerns about the quality of schools and finding jobs.

“So much of this we can take care of,” Trump told them.

(Additional reporting by Emily Stephenson in Greenville, Jeff Mason in Tampa and Alana Wise and Ginger Gibson in Washington; Editing by Leslie Adler)