Mongrels aired for the first time on Tuesday but the creators of Pets have now complained that it borrowed from their programme.
Writing on the BBC's TV blog, Pets creator Brian West said that puppeteers Iestyn Evans and Andy Heath had worked on both shows and claimed that the producers of Pets had pitched a spinoff to the executive producer of Mongrels in 2005.
He continued: "You might also recognise Vince in Mongrels. He's Trevor from Pets. At the last count, Pets had over ten million downloads on iTunes, so I don't think it'll be long before other people notice these little coincidences."
Meanwhile, Chortle reports that the makers of Pets have received 30 emails from viewers pointing out the similarities.
However, West later wrote that Mongrels executive producer Stephen McCrum had assured him that Pets was not discussed during the making of the BBC Three show.
Heath also defended the programme, posting: "It is regretful that this comparison is made, as having been involved with both projects myself from conception, I feel like our hard work is being taken advantage of.
"Pets was Pets. Mongrels is Mongrels. If, as a viewer, you can sit down and say they are the same, then there is little point in making any new shows if the slightest similarity (puppets and animals) can be suggested as idea stealing. I am surprised Basil Brush hasn't been on the blower, as he is a fox, and that must be a copy, right?"
He added: "I worked on both, and know for a fact where they both come from. Two very different ideas."
A BBC spokesperson told DS: "We Are Mongrels is entirely created and devised by Adam Miller and writers Jon Brown and Daniel Peak with the BBC, drawing inspiration from animation and puppetry of many kinds. It is a new and original production."
Mongrels continues on Tuesday at 10.30pm on BBC Three.