The comments were made on ABC's Q& program on Monday, August 18, after Palmer was questioned over his long legal battle with China's CITIC Pacific.
In a letter to Chinese Ambassador to Australia Ma Zhaoxu, Palmer said he sincerely apologised for any insult to the Chinese people.
"I regret any hurt or anguish such comments may have caused any party and I look forward to greater understanding for peace and cooperation in the future," Palmer wrote.
Palmer urged people to keep an "open mind"
"In keeping an open mind, I now come to the realisation that what I said on Q& was an insult to Chinese people everywhere and I wish to assure them they have my most genuine and sincere apology, that I am sorry that I said the things I said on the program," he said.
Palmer went on to write that it was in the interest of the world that Australia and China had a good relationship and urged citizens of both countries to work together.
The comments caused widespread criticism of Palmer from all sides of politics, as well as business and lobby groups.
Western Australian Mines Minister Bill Marmion told a Morgans breakfast in Perth last week that he found the comments "shocking"
"I was staggered by the comments Clive Palmer made," he said.
Marmion said the comments were "unhelpful" and put billions of Chinese investment in WA's mining sector at risk, echoing concerns aired by the WA Chamber of Minerals & Energy.
"When [the Chinese] see a politician come out and make those comments … it's mindboggling," he said.
"The way [Palmer's] been behaving, through litigation with CITIC Pacific, hasn't been helpful either.
"If the CITIC Pacific investment doesn't go well, it doesn't bode well for Chinese investment."
BHP Billiton CEO Andrew Mackenzie and Fortescue Metals Group CEO Nev Power separately played down the impact of the comments last week.
"It just sounded like a bit of ranting and raving and I'm sure the Chinese will dismiss [Palmer's comments] for what they are," Power said on a teleconference.
"I heard both the Opposition and government distance themselves from the comments and make it very clear where Australia stands and that goes for Fortescue."