Nandy said the register had been rushed out just weeks ahead of the general election and that it commanded no support from the public, transparency campaigners or lobbyists.
The MP claimed registrar Alison White earns £120,000 a year, which was "a waste of money" because her job would be to oversee a register with just 75 registrations.
Nandy said: "This register is being rushed out before an election and is widely discredited. It would do nothing to shine a spotlight on any of the recent scandals that have beset this Government. It's backed by no code of conduct, no sanctions and the Government's own lobbying tsar thinks only 75 lobbyists will register."
Nandy said the Labour Party was "committed" to a universal register including those who lobby regional government as well as a code of conduct, backed by sanctions.
She added: "Labour will push for [the register] to be scrapped and replaced with a comprehensive register, backed by sanctions, that has the support of transparency campaigners and the public."
Nandy’s comments drew support from Iain Anderson, chairman of the APPC.
He said: "Labour is right to call for a universal register including all government relations professionals – this is what we have been calling for from the start. A new government needs to reform this fatally flawed statutory register, which will do nothing for lobbying transparency."
White told PRWeek that she would be writing to Nandy by the end of this week but that she did not recognise the basis for the her remarks.
"I have no idea what the evidence is that the register is a mess. There are different views about the legislation but my role is to ensure that those who are required to sign the register, as is, do so."
White denied that she had said there would only be 75 firms registered by the time the register was published in the final week of March and said that this was the assessment of the industry.
So far, only 20 firms are registered, White added.
She continued: "The legislation contains both civil and criminal sanctions for non-compliance. As for my remuneration, at the time the post was advertised, this was for £420 per day and I work one-and-a-half days a week. I have taken care to ensure my office is run cost-effectively."
White said she would publish details of the running costs of her office next week.