Whatever the similarities between Mr Mandelson and a crustacean with fiercesome claws that approaches its prey sideways on, the unguarded observation provoked a flurry of "clarifications" from Downing Street and totally overshadowed the Deputy Prime Minister's original errand.
Mr Prescott had gone to the millennium exhibition site to announce the creation of a wildlife-friendly flood defence scheme for the Thames. But then he christened the photocall crab Peter and asked it: "Do you think you'll get on the Executive Peter?"
Mr Mandelson is bidding for election to Labour's ruling National Executive Committee and Mr Prescott hardly sounded to be wishing him well. The jibe was seized on by reporters as further evidence of tension between the two men over Mr Mandelson's high-profile role while Tony Blair has been on holiday.
Later attempts by Mr Prescott to "clear up any misunderstanding" were heavier on puns than sincerity. "I wish Peter Mandelson all the best in his attempt to claw his way on to the NEC. I hope that his pincer move goes well because under his hard shell he has a soft heart."
The two colleagues were also at odds over the disclosure that a key part of the millennium dome is to be built in Germany. Mr Prescott upset builders by saying the award of a pounds 6m contract to Koch Konstruktive Membrane of Munich was "a sad reflection on the competence of the [British] industry".
But Mr Mandelson, the minister in charge of the dome project, said it was a "success story" for British industry. "I am not disappointed really ... because overwhelmingly the huge bulk of work and the value of what we are doing at Greenwich is being taken up by British companies,"he told BBC Radio WM.