The public affairs association made these calls in its response to a public consultation launched by the Office of the Registrar of Consultant Lobbyists last month.
According to the APPC's consultation reply, the registrar must take action to "identify those registrants incorrectly declaring adherence to the APPC Code of the Conduct, which can be claimed only by members of the APPC".
It said that this apparently deliberate false claim was made by two agencies on the register in November. The APPC declined to identify the agencies involved - but said these incorrect claims had been taken down by the regulator after the association flagged them up.
The APPC's consultation reply also asked that the legislation governing the lobbying register be changed, such that the register is expanded to include lobbyists and government relations professionals working for law firms and management consultancies, alongside those working for more conventional lobbying or public affairs agencies.
It said the APPC had been given assurances by then minister Tom Brake, a Liberal Democrat, in April 2014 that the register would "apply to any and all persons or firms acting as a consultant lobbyist".
"We feel that the registrar should be focusing most attention on those organisations that should be registered but have not done so and therefore continue to act outside the law. This risk-based approach should be used to best define the actions of the registrar in relation to consultant lobbying and in allocating the resources of the office," the APPC response said.
The response also said the APPC saw "no merit" in creating a new voluntary code of conduct for lobbyists, given the proliferation of codes currently in existence, and it felt there was "continuing need for clarity and guidance from the registrar to the industry". It said that the APPC "would welcome assisting the registrar in this process".
The consultation closes on 31 December.