Speaking on the steps of the Lincoln Memorial in Washington DC, Donald Trump also pledged to bring change.
Among attendees at the two-hour event were his family, actor Jon Voight and Soul Man singer Sam Moore.
President-elect Donald Trump earlier laid a wreath at Arlington National Cemetery, Virginia.
Make America Great Again! Welcome Celebration on January 19 was open to the public and featured performances by country stars Toby Keith and Lee Greenwood.
In brief remarks at the end of the concert, Donald Trump said: “We’re going to unify our country.
“We’re going to make America great for all of our people. Everybody, everybody, throughout all of our country. That includes the inner cities.”
Donald Trump’s supporters have been streaming into Washington DC, and he reminded them that many had doubted the campaign’s chances of success.
“They forgot about a lot of us,” he said.
“On the campaign, I called it the forgotten man and the forgotten woman. Well, you’re not forgotten anymore.”
Pledging to bring back jobs, build up the military and strengthen the border, Donald Trump added: “We’re going to do things that haven’t been done for our country for many, many decades.
“It’s going to change, I promise you. It’s going to change.”
Donald Trump’s first stop on January 19 was at his Trump International hotel, located just blocks from the White House.
Donald Trump appeared with his wife Melania at a luncheon for members of his incoming administration.
Melania Trump briefly spoke, telling the crowd: “Tomorrow we’re starting the work.”
Donald Trump told the crowd in the presidential ballroom: “We have a lot of smart people. I tell you what, one thing we’ve learned, we have by far the highest IQ of any cabinet ever assembled.”
He hinted that Woody Johnson, owner of the New York Jets NFL team, would be US ambassador to the UK.
After the welcome concert, Donald Trump spent the night at Blair House, the presidential guest residence located just steps from the White House.
He is due to be sworn in at noon on Friday, January 20.
Despite Donald Trump’s appeal for unity, billionaire investor George Soros launched a stinging attack on him.
Speaking at the World Economic Forum in Davos, George Soros labeled Donald Trump “an imposter, a conman and a would-be dictator”.
Donald Trump has nominated all 21 members of his cabinet as well as six other roles that require Senate confirmation, according to his team.
The Republican-controlled Senate is expected to vote on January 20 to confirm General James Mattis, the defense secretary nominee, and retired General John Kelly, the pick for Homeland Security.
Donald Trump has asked about 50 senior Obama administration officials to stay on until they are replaced, spokesman Sean Spicer told a news conference.
They include Brett McGurk, the special envoy to the US-led coalition fighting the so-called Islamic State, as well as Deputy Defense Secretary Robert Work.
Down the road at the White House, President Barack Obama spent his last day in office with the daily briefing and lunch with Vice-President Joe Biden.
Barack Obama also spoke to German Chancellor Angela Merkel in his final conversation with a foreign leader as president, according to the White House.
First Lady Michelle Obama and Angela Merkel’s husband, Joachim Sauer, also joined the call.
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