The pair have set up a Facebook page to find four finalists to perform in a Kennel Club Crufts Factor heat at the Discover Dogs show in Earls Court on November 10.
No matter how strange or obscure their talent, members of the public are being urged to enter the competition, which has a top prize of entry into the world's most prestigious dog competition Crufts.
Another secondary prize may also be on offer - producers of Simon Cowell's one-off dog talent show Take the Lead will also be present, scouting for potential entrants.
The heat will be judged by Johnny Ball, and Joanne Good and Anna Webb from BBC Radio London.
Butler said of the talent search: "Dogs have an amazing ability to learn all sorts of skills, so it is really exciting to see the launch of a competition that is solely dedicated to celebrating dogs and their talents.
"Pudsey has always adored performing and working with me as a team and it was great to give him the chance to show his skills to the nation. Crufts Factor gives all dogs the same opportunity."
Take the Lead will air on ITV1 over the Christmas period.
Watch Ashleigh & Pudsey's audition on Britain's Got Talent below: