The new Rent Smart scheme requires anyone who rents out property in Wales to register or become licensed by 23 November.
But the Residential Landlords Association (RLA) said many were still unaware they need to do so.
Rent Smart Wales said landlords were given a year to register and it would not extend the deadline.
A Freedom of Information request by the RLA showed just 32,230 out of 130,000 landlords had registered by 18 October - those who do not comply can be fined.
The figures were released by Cardiff council, which is administering the scheme for the whole of Wales.
Douglas Haig, RLA director for Wales, said he was writing to Community Secretary Carl Sargeant to request a new deadline to allow time for landlords to be properly educated about what they need to do.
But Rent Smart Wales said there had been a large increase in numbers registering as the deadline approached and 46,300 out of 130,000 landlords had now registered and a further 11,400 had begun the registration process.
Mr Haig said communication had been "poor" with "very few" landlords aware of the scheme.
He said others were leaving it until the last minute because registration and licences run for five years from the date they are approved, not from 23 November.
The number of staff employed to carry out the scheme had also been "grossly underestimated", he added.
"I don't think it's asking a lot for the Welsh Government or Cardiff council to come forth with an education plan to get this information out there. That would be a sensible approach," he said.
A Rent Smart Wales spokesman said: "We have no intention of extending the deadline. However, we do recognise that, due the very high numbers of landlords visiting the website to register and apply for licenses, some are experiencing difficulties.
"The Rent Smart Wales team consists of 79 posts and the team are working hard to reduce waiting times for customers.
"Once the November 23 deadline for complying has passed, enforcement powers will be used in a sensible and proportionate manner."
RENT SMART FACTFILE:
Calls have been made for an extension to the registration deadline for all residential landlords in Wales.