David Lappartient, who was elected head of the UCI in September last year, was responding to the fact that five-time Olympic gold medallist Wiggins has included Armstrong in a book about the most influential figures in his life.
The excerpt compliments Armstrong's character and sporting exploits. Wiggins said at the Rouleur Classic in London this week that he still speaks to the American who was stripped of seven Tour de France titles in 2012 and banned for life by the U.S. Anti-Doping Agency after orchestrating a doping scheme.
"Bradley Wiggins is Bradley Wiggins so he says some strange things sometimes," the Frenchman told reporters in London on Friday.
"But, when I saw that I thought it was unbelievable, that the guy who won the Tour de France, has been an Olympic champion, has been a world champion and he is (now) supporting Lance Armstrong that has been banned for life for cheating.
"For me, this is unacceptable to have some statement like this from a former winner of the Tour de France."
Speaking on stage at the Rouleur Classic on Thursday Wiggins said of Armstrong: "He's a tough character. I know him quite well. I still speak to him, sorry about that, but I can't change it," he said.
"This isn't to condone anything he did. He knows he did wrong. But at some point, you've got to get on with your life."
Cycling was tainted when Armstrong, who had long denied using performance-enhancing drugs, admitted to doping in January 2013. The UCI has been trying to mend the sport's reputation ever since and Lappartient said cycling was now "leading the bunch" in the fight against doping.
He was, however, disappointed with the lack of progress on trying to get pain-killer Tramadol on the World Anti-Doping Agency's list of banned substances in 2019.
Some experts believe that Tramadol can have performance-enhancing benefits. It is on a WADA monitoring list and reports by the body have shown that its use in cycling vastly outweighs its use in other sports.
Lappartient was hopeful that the UCI could prohibit the drug for use in competition on medical reasons by early next year.
"If you need Tramadol, no problem, then you will not be able to ride or take part in a race. I don't think it's appropriate in other cases," he said.
Lappartient succeeded Briton Brian Cookson as president of the UCI in Bergen last year, becoming the first Frenchman to take charge of the global body since Achille Joinard between 1947 and 1957.
Following his election, he said that he wanted to see a women's Tour de France within his first term of office.
However, this year the Tour organisers Amoury Sport Organisation reduced their women's race, La Course, from a two-day event in 2017 to one day.
La Course will remain a single day event next year and Lappartient said he was putting pressure on organisers to increase their efforts in the fight for gender equality.
"I think one day is not enough... I met with the Tour de France to discuss most specifically about women's cycling and I said to them 'I think you are the leading organisation in the world, so you have to take your part of responsibility regarding support for women's cycling,'" he said.