The 86-year-old enraged viewers with his off mic sexist comments about Ms Akins during coverage of the Masters in Augusta.
As the BBC showed images of Mr Garcia’s fiancee, 31, the presenter could be heard saying: “She’s got the shortest skirt on campus.”
And many have now taken to social media to demand his resignation, claiming he ruined the golfer’s big moment with his “disgraceful comment”.
The Masters was watched by more than 2.5 million people who sat on the edge of their seats as the Spaniard narrowly held off Briton Justin Rose in a captivating final.
Angela Akins looked stunning in a cobalt blue skirt as she supported partner Sergio Garcia
The comment has come as a shock to many – but it was actually the second time in a week Alliss was accused of sexism following a discuss on Newsweek about women “not being able to do things men do”.
The sports personality said: “Women will never be able to do things that men can do.
“If we want to be equal, are you going to get a woman fighting for the heavyweight championship of the world [in] boxing?
Angela Atkins was at the Masters to support her Spaniard fiancee
The couple's wedding is planned for the week after the Open at Birkdale in July
“I don’t like to see women punching each other in the chest. I think it will cause irreparable damage.”
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He stressed his comments were just about physical differences, claiming he wasn’t talking about “lawyers or accountants”.
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Women will never be able to do things that men can do
Golf pundit Peter Alliss
But he also provoked further anger after adding: “I think women are more delicate than men. I like holding chairs for women.
“I don’t care for macho women and yet they’re prevalent today.”
Alliss was heard saying: “She’s got the shortest skirt on campus.”
Peter Alliss has worked for the BBC since 1961
The sport anchor, who has worked for the BBC since 1961, has also faced previous accusations of sexism.
During the 2015 Open tournament he said US golfer Zach Johnson’s wife was “probably thinking, if this goes in I get a new kitchen.”
A BBC spokesperson said: “Whilst believing he was off air Peter made a light-hearted remark which he now knows was inappropriate.”