US President-elect Donald Trump said Thursday he has picked the tough-talking retired general James Mattis to be his defence secretary as he soaked up adulation at a buoyant Ohio rally that recalled this year's rough-and-tumble campaign.

The splash of hard news came during a sea of soaring — and then blunt — rhetoric from the 70-year-old Republican billionaire, who was speaking at his first post-election event following days of meetings about forming his cabinet.

“We are going to appoint 'Mad Dog' Mattis as our secretary of defence,” Trump told cheering supporters in Cincinnati, referring by nickname to the retired four-star Marine general who headed the US Central Command, with authority over US troops in Iraq and Afghanistan.

“He's our best. They say he's the closest thing to (World War II) general George Patton that we have,” Trump said, divulging his pick ahead of schedule after his transition team said there would be no more cabinet announcements this week.

Mattis will require both Senate confirmation and a special waiver of a law that bans uniformed military officers from serving as secretary of defence for seven years after leaving active duty.

At least one Democrat, Senator Kirsten Gillibrand, already signalled she will oppose the waiver.

“Civilian control of our military is a fundamental principle of American democracy,” the senator tweeted from New York.

Trump's surrounding himself with military figures — he has picked retired lieutenant general Michael Flynn to be his national security adviser and is considering retired general David Petraeus for secretary of state — has unnerved some observers who point to America's long tradition of civilian government.

Adam Schiff, the ranking Democrat on the House Intelligence Committee, praised Mattis' “knowledge, experience and leadership” but also expressed concerns about the precedent being set.

“That concern would be further heightened should the president-elect nominate any further military personnel to high positions of civilian leadership in his administration,” he said.

'No choice' but unify

At the start of his address, Trump launched lofty appeals to unite what he called a “very divided nation” and reject “bigotry and prejudice in all of its forms.”

Americans will “come together — we have no choice, we have to,” he added.

On the economy, “Americans will be the captains of their own destiny once again,” he promised.

He even vowed to try to work with Democrats to end gridlock in Congress.

But the Manhattan property mogul, who defeated Hillary Clinton last month to win the White House, dramatically returned to the abrasive tone that marked his controversial and ultimately victorious campaign.

He savaged the nation's “extremely dishonest” press, slammed illegal immigration and the country's refugee programme, mocked his critics and vowed to “drain the swamp” in establishment-heavy Washington.

It became a loose, swerving speech that kicked off what his team has branded a “thank you tour” — a victory lap of sorts that will take him to several political battlegrounds including Ohio, perhaps the nation's ultimate swing state.

“I love you Ohio!” the populist political novice said to a loud cheer from a crowd that filled roughly half the US Bank Arena, which has a capacity of around 17,000.

Trump lamented the roadblocks surrounding the venue, which he said had depressed attendance.

Earlier, the president-elect, who made guaranteeing jobs for blue-collar US workers a key campaign plank, strode triumphantly through an Indiana factory that makes Carrier air conditioners, trumpeting a deal to keep 1,100 manufacturing positions from moving to Mexico.

He then starkly warned other US firms that they will face “consequences” if they relocate abroad.

“The era of economic surrender is over,” Trump said.

“We're going to fight for every last American job. It is time to remove the rust from the rust belt and usher in a new industrial revolution.”

'Buy American, hire American'

During the race, the Republican billionaire threatened to slap tariffs on firms that decamped for places like Mexico or Asia, where labour and other costs are cheaper.

“Buy American and hire American,” he said in Ohio.

“That will be our new mantra.”

Carrier has announced it will preserve more than 1,000 jobs and continue to manufacture gas furnaces in Indianapolis, thanks to $7 million in state incentives negotiated with the help of Trump and Vice President-elect Mike Pence, Indiana's governor.

Several hundred jobs will still move to Mexico.

“What happened today in Indiana, we're going to do that all over the country,” he said in Cincinnati.

The White House avoided criticising Trump's effort, saying saving jobs is laudable, but expressed scepticism about the strategy of keeping jobs in America one company at a time.

“Mr Trump would have to make 804 more announcements just like that to equal the standard of jobs in the manufacturing sector that were created in this country under President Obama's watch,” White House spokesman Josh Earnest said.