US President-elect Donald Trump met with the eldest son of the late civil rights hero Martin Luther King Jr. amid tensions escalating between the the New York magnate and prominent African-American leaders.

Martin Luther King III said that he had "a very constructive meeting" with the president-elect and touched on how he hopes to be a "bridge-builder" to help the country "become a greater nation" moving forward, ABC News reported.

The private meeting that took place on Monday evening at the Trump Tower in New York, comes after the president-elect was criticised over the weekend for sparring with African American Congressman and civil rights icon John Lewis who had marched with Martin Luther King Jr. at Selma and other key civil rights protests.

Trump attacked Lewis on Twitter after the Georgia Democrat told NBC News that he was not attending the President-elect's inauguration on January 20 and that he did not view Trump as a "legitimate president".

Martin Luther King III did not criticise Trump directly, saying that in the "heat of emotion, a lot of things get said on both sides".

"The goal is to bring America together," he said.

Earlier on Monday, Trump's incoming press secretary, Sean Spicer, announced on Twitter that the president-elect would meet with Martin Luther King III, as the nation observes the federal holiday honouring Martin Luther King Jr, ABC News reported.

Trump on Monday morning said: "We should honour Martin Luther King for being the great man that he was!"

"Celebrate Martin Luther King Day and all of the many wonderful things that he stood for," Trump said on Twitter.