A council leader has distanced himself from a tweet made by his party suggesting a family can be fed on £10 a week.
The tweet, which has now been deleted, said parents who could not meet this budget were "indolent or dysfunctional or more likely parents who simply don't know how to feed their children well".
It has enraged food writer Jack Monroe who was tagged in the original post.
Tim Warren said Bath's Conservatives had now tweeted an apology.
The original tweet, which appeared on Saturday, on the Bath Conservatives Association feed, said: "The reality may be indolent or disfunctional (sic) parents or more likely parents who simply don't know how to feed their children well.
"If absolutely-not-a-Tory Jack Monroe @BootstrapCook could feed herself & her child for £10 a week - not easily, but adequately - most people can."
The campaigner and cookbook author is renowned for a blog about cooking for a family on a shoestring.
Reacting on the blog, Monroe said: "I took exception to the Conservatives holding me up as some kind of role model because, it was their policies that left me hungry, cold, almost homeless, moving house seventeen times with a child under my arm."
Monroe challenged the original tweeter to live on just £10 a week for three weeks running, but added: "You won't even start to experience the daily grind of living in poverty.
"Poverty isn't just having no heating, or not quite enough food, or unplugging your fridge and turning your hot water off.
"Poverty is the sinking feeling when your small boy finishes his one weetabix and says 'more mummy, bread and jam please mummy' as you're wondering whether to take the TV or the guitar to the pawn shop first, and how to tell him that there is no bread and jam."
Mr Warren, leader of BANES council, said he did not agree with the contents of the original tweet and it was "ill-judged" and "outrageous".
Someone tell @BathCA that I, feckless and indolent single mother (and bestselling cookbook author) am having a ready meal for my dinner tonight because it is CHEAPER than buying all the component parts to make a dinner for one. Thanks. pic.twitter.com/KoGrTvS3eL— jack monroe |🍴📚 (@BootstrapCook) February 17, 2018
"This does not reflect the view of my cabinet or the wider Conservative party," he said. "Sometimes people tweet things which we have no control of. I've got two boys and you can't feed a family for £10 a week."
A single thoughtless tweet on food poverty, not intended to insult, but insulting nonethless, for which we unreservedly apologise, does not represent our Association view, nor our continuing committment to build a better Britain & a better Bath for all residents.— Bath Conservatives (@BathCA) February 19, 2018