U.S. President Barack Obama "was born here," Bloomberg said on "Fox News Sunday." And Trump, exploring a 2012 U.S. presidential run, could hurt his prospective candidacy by associating with people arguing otherwise, he said.
"I think the Republicans are making a terrible mistake in making this a big issue," Bloomberg said of the conspiracy theories Obama is not a natural-born citizen and is therefore not eligible to be president.
Some "birthers" allege Obama was born in Kenya, not Hawaii, or that his birth certificate is a forgery. Others allege he's a citizen of Indonesia or that because he had dual British and U.S. citizenship at birth, he is not a natural-born citizen.
Chester Arthur, a Republican U.S. president from 1881 to 1885, was also a British subject as well as a U.S. citizen at birth.
Bloomberg, a political independent, said Republicans should focus on important issues rather than the birther conspiracy theory.
"We have immigration. We have the deficit. We have the economy," he said. "Those are the things that the public cares about. My girlfriend always says that it's all about housing and jobs -- my house, my job. That's what the public cares about. If the Republican Party doesn't start addressing that, they will lose and they deserve to."
Bloomberg girlfriend Diana Taylor, a former New York state banking superintendent, has said she might run for U.S. Senate from New York in 2012.
Bloomberg said Sunday he felt Obama still had time to reach across party lines to help solve the nation's big problems.
"The president's got to start inviting people over for dinner," Bloomberg said. "He's got to play golf with them. He has to pick up the phone and call and say, 'I know we disagree on this, but I just want to say, I heard it was your wife's birthday or your kid just got into college.'"
"He has to go build friendships," Bloomberg said of Obama. "That's what an executive's job is, and the president is a people person. He knows how to deal with people."
Trump had no immediate response to Bloomberg's remarks.
After GOP strategist Karl Rove said Tuesday Trump's birther focus made him "a joke candidate," Trump called Rove "a loser" who "should go into retirement where he belongs."
Rove "is doing the Republican Party a great disservice by trying to stop the discussion about the president not being able to present his birth certificate to the American people -- or to assure the American people as to his place of birth," Trump told conservative news organization Newsmax Media. "This is a great issue for Republicans, and I can tell you that the president is spending millions of dollars fighting this issue and he doesn't like it at all.
"I also have great respect for the states considering legislation that would require a birth certificate, not a certificate of live birth, be mandatory in order for a candidate to appear on a presidential ballot in their state," Trump said.