Trump said the Golden State Warriors were no longer invited to the White House after star player Curry, 29, said he did not want to attend.
"Going to White House was an honour until you showed up," James, 32, said.
On Friday, Trump said NFL players who protest during the national anthem should be sacked.
James, who plays for the Cleveland Cavaliers and has won three NBA championships and four NBA MVP awards, campaigned for Democrat candidate Hillary Clinton, Trump's rival, during the 2016 presidential election campaign.
Basketball's champion team, the Golden State Warriors from California, were considering turning down the traditional invitation to celebrate their NBA title success at the White House.
Warriors point guard Curry, a two-time winner of the NBA's Most Valuable Player award, said the team could "inspire some change" by refusing to visit the home of the president.
"I don't want to go," Curry said on Friday, adding that it would show the players "don't stand for... the things that he's said and the things that he hasn't said in the right times".
He added: "I don't think us not going to the White House is going to miraculously make everything better, but this is my opportunity to voice that."
Trump responded by tweeting that the invitation had been withdrawn.
The Warriors later said they will travel to Washington in February without a presidential invite to "celebrate equality, diversity and inclusion".
Last year, NFL quarterback Colin Kaepernick refused to stand for the anthem in protest at racial injustice and police brutality.
More players have since joined in by taking a knee or raising a fist during the anthem.
Trump told a Republican rally in Alabama on Friday that a refusal to sing the anthem showed "disrespect of our heritage".
"Wouldn't you love to see one of these NFL owners, when somebody disrespects our flag, to say, 'Get that son of a bitch off the field right now, out, he's fired'," he said.
"Some owner is going to do that. He's going to say, 'That guy that disrespects our flag, he's fired.' And that owner, they don't know it [but] they'll be the most popular person in this country."
National Football League commissioner Roger Goodell said players had raised millions of dollars for recent disaster relief efforts and were involved in community programmes.
"There is no better example than the amazing response from our clubs and players to the terrible natural disasters we've experienced over the last month," he said.
"Divisive comments like these demonstrate an unfortunate lack of respect for the NFL, our great game and all of our players, and a failure to understand the overwhelming force for good our clubs and players represent in our communities."
NFL Players Association president Eric Winston said: "I am extremely disappointed in the statements made by the president last night.
"The divisiveness we are experiencing in this country has created gridlock in our political system, given voice to extreme, fringe beliefs and paralysed our progress as a nation.
"Divisiveness breeds divisiveness but NFL players have proven to unify people in our country's toughest moments."
Trump also encouraged NFL fans to walk out of the stadium if they see players protesting during the pre-game anthem.
Detroit Lions tight end Eric Ebron said: "Does anyone tell Trump to stick to politics, like they tell us to stick to sports?"
Having opted out of his contract with the San Francisco 49ers in the off-season, Kaepernick remains a free agent. The 29-year-old said he began his protests because he wanted to start a nationwide debate.
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