The 51-year-old was widely criticised last week when he suggested on the BBC One programme that workers taking industrial action over pension reforms should be executed "in front of their families".
According to the latest update, 31,057 people have complained about the incident, an increase of around 10,000 on the complaints figure of more than 21,000 published last Friday.
Clarkson's One Show appearance has now attracted more complaints than the 'Sachsgate' scandal on BBC Radio 2 in 2008, when Jonathan Ross and Russell Brand left lewd messages on the voicemail of Andrew Sachs, provoking 27,000 complaints.
Last week, public sector trade union UNISON described Clarkson's comments as "appalling" and confirmed that it was taking urgent legal advice over his behaviour.
The statements were also criticised as being a "bit silly" by prime minister David Cameron, a friend of the Top Gear presenter, and labelled "disgusting" by Labour leader Ed Miliband.
Clarkson later indicated his intention to apologise for the remarks, but suggested that he had been misinterpreted and was actually poking fun at the BBC.
At the weekend, he provoked another controversy by describing people who kill themselves as "selfish" in his newspaper column.
He first made the comments in the One Show appearance on Wednesday, but this was overshadowed by the outcry over his remarks about public sector workers.
Undeterred by the controversy, Clarkson opted to expand on his views about railway suicides in his regular column in The Sun, calling on trains to continue their journey after the death and leave the body parts to scavenging animals.