Williams, a lifelong Republican whose hits include Moon River and Music To Watch Girls By, told the Radio Times he thought Mr Obama wanted to turn the US into a “socialist country”.
The 81-year-old was a friend of the Kennedy family during the 1960s and was present at the Los Angeles rally where Robert F Kennedy was assassinated in 1968.
“I was very close to Bobby and he asked me to be a delegate for him when he ran for president,” he said.
“He knew about me being a Republican, but just laughed and said, ‘Sign yourself in as a Democrat and then change back afterwards’. Sadly, I never got to do that.
“I was very close to Teddy Kennedy, too, and his death recently brought it all back. What a tragedy. Had he lived, I think Bobby would have been a great president.”
But Williams had a less favourable opinion of the current president.
“Don’t like him at all,” he said, “I think he wants to create a socialist country. The people he associates with are very Left-wing. One is registered as a Communist.
“Obama is following Marxist theory. He’s taken over the banks and the car industry. He wants the country to fail.”
Politicians, media personalities and conservative activists have accused the US president of espousing socialist ideas.
Earlier this month, Jim Greer, the chairman of the Republican Party in Florida, said he was “absolutely appalled that taxpayer dollars are being used to spread President Obama’s socialist ideology”, after the US leader appeared in a televised address to be shown in classrooms around the country.