BURBANK, California — US President Barack Obama lampooned Donald Trump, saying the real estate tycoon's feud with him dated back to "when we were growing up together in Kenya."

Obama ribbed the flamboyant mogul during an appearance on "The Tonight Show with Jay Leno" after Trump revived the right-wing conspiracy theory that alleges that the president was not born in the United States.

"This all dates back to when we were growing up together in Kenya," Obama joked, after dashing to California to record the show, to be broadcast later Wednesday on NBC, as part of a 40-hour campaign sweep through eight states.

"We had constant run-ins on the soccer field, he wasn't very good and resented it," said Obama, who is the son of a white American mother and Kenyan father who was born in Hawaii.

"When we finally moved to America, I thought it would be over," the president said, with a beaming grin, and admitted he had never actually met Trump.

The flamboyant real estate tycoon and reality TV host had earlier whipped up media attention by promising a "very, very big" announcement to be made on his Twitter and Facebook accounts.

But, "The Donald," as he is popularly known, made no real news whatsoever in his hotly awaited appearance.

The five-minute statement simply revisited the "birther" conspiracy theory, which claims that Obama was born outside the United States and is therefore occupying the White House illegitimately.

Trump demanded that the president release his college and passport records, saying that if this happened by October 31 he would donate $5 million to a charity of Obama's choice.

Obama also joked with Leno that the difference between debating his Republican foe Mitt Romney and his wife was that "with Michelle I concede every point," but admitted he had failed to connect with Americans in his lackluster first debate in early October.

"Clearly, I had a bad night because the whole point of these debates is to make sure the American people understand the stakes," Obama said.

"If you don't have the energy and the presentation that makes people snap up and say 'I get it.' You are not doing your job."

Obama also said that the context of the presidential debates was an artificial situation, but quipped that he got better as he went along in the trio of clashes with his Republican foe.

He also offered his prediction for Major League Baseball's World Series, which kicked off on Wednesday night.

He said the San Francisco Giants were a great team, but said he was rooting for the Detroit Tigers, faultlessly switching the conversation to his rescue of the Big Three auto makers, which is one of his proudest achievements.

"I didn't want Detroit to go bankrupt," Obama said, playing off the headline of an article that Romney wrote for the New York Times opposing his bailout of the car firms which read "Let Detroit Go Bankrupt."